Function

Problem 301

The circumference CC of a circle is a function of its radius given by C(r)=2πrC(r)=2 \pi r. a. Express the radius of a circle as a function of its circumference. Call this function r(C)r(C).
Enter the exact answer.
Enclose numerators and denominators in parentheses. For example, (ab)/(1+n)(a-b) /(1+n). r(C)=r(C)= b. Find r(34π)r(34 \pi) and interpret its meaning. r(34π)=r(34 \pi)= \square Number

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Problem 302

Find the inverse of the function on the given domain. f(x)=(x4)2,[4,)f(x)=(x-4)^{2},[4, \infty)

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Problem 303

Find the inverse of the function. f(x)=95x3f(x)=9-5 x^{3}
Hint: The cube root is the same as an exponent of 1/31 / 3, so for 19x3\sqrt[3]{19 x}, you could type in (19x)(1/3)\left(19^{*} x\right)^{\wedge}(1 / 3). Remember your parentheses!

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Problem 304

3. 求下列函数的微分: (1) y=1x+2xy=\frac{1}{x}+2 \sqrt{x} (2) y=xsin2xy=x \sin 2 x (3) y=xx2+1y=\frac{x}{\sqrt{x^{2}+1}}; (4) y=ln2(1x)y=\ln ^{2}(1-x) ; (5) y=x2e2xy=x^{2} \mathrm{e}^{2 x}; (6) y=excos(3x)y=\mathrm{e}^{-x} \cos (3-x); (7) y=arcsin1x2y=\arcsin \sqrt{1-x^{2}}; (8) y=tan2(1+2x2)y=\tan ^{2}\left(1+2 x^{2}\right); (9) y=arctan1x21+x2y=\arctan \frac{1-x^{2}}{1+x^{2}} (10) s=Asin(ωt+φ)(A,ω,φs=A \sin (\omega t+\varphi)(A, \omega, \varphi 是常数 )).
4. 将适当的函数填人下列括号内,使等式成立: (1) d()=2 dx\mathrm{d}(\quad)=2 \mathrm{~d} x; (2) d()=3xdxd(\quad)=3 x d x (3) d()=cost dt\mathrm{d}(\quad)=\cos t \mathrm{~d} t (4) d()=sinωxdx(ω0)d(\quad)=\sin \omega x d x \quad(\omega \neq 0); (5) d()=11+x dx\mathrm{d}(\quad)=\frac{1}{1+x} \mathrm{~d} x (6) d()=e2xdxd(\quad)=e^{-2 x} d x (7) d()=1x dxd(\quad)=\frac{1}{\sqrt{x}} \mathrm{~d} x (8) d()=sec23x dxd(\quad)=\sec ^{2} 3 x \mathrm{~d} x.

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Problem 305

3. 求下列函数的微分: (1) y=1x+2xy=\frac{1}{x}+2 \sqrt{x}; (2) y=xsin2xy=x \sin 2 x (3) y=xx2+1y=\frac{x}{\sqrt{x^{2}+1}}; (4) y=ln2(1x)y=\ln ^{2}(1-x) ; (5) y=x2e2xy=x^{2} e^{2 x}; (6) y=excos(3x)y=\mathrm{e}^{-x} \cos (3-x) (7) y=arcsin1x2y=\arcsin \sqrt{1-x^{2}}; (8) y=tan2(1+2x2)y=\tan ^{2}\left(1+2 x^{2}\right); (9) y=arctan1x21+x2y=\arctan \frac{1-x^{2}}{1+x^{2}}; (10) s=Asin(ωt+φ)(A,ω,φs=A \sin (\omega t+\varphi)(A, \omega, \varphi 是常数 )).
4. 将适当的函数填人下列括号内,使等式成立: (1) d()=2 dx\mathrm{d}(\quad)=2 \mathrm{~d} x (2) d()=3xdxd(\quad)=3 x d x (3) d()=cost dt\mathrm{d}(\quad)=\cos t \mathrm{~d} t; (4) d()=sinωxdx(ω0)d(\quad)=\sin \omega x d x \quad(\omega \neq 0); (5) d()=11+x dx\mathrm{d}(\quad)=\frac{1}{1+x} \mathrm{~d} x; (6) d()=e2xdxd(\quad)=e^{-2 x} d x; (7) d()=1x dx\mathrm{d}(\quad)=\frac{1}{\sqrt{x}} \mathrm{~d} x; (8) d()=sec23x dx\mathrm{d}(\quad)=\sec ^{2} 3 x \mathrm{~d} x.

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Problem 306

Find the inverse of the function on the given domain. f(x)=(x4)2,[4,)f(x)=(x-4)^{2},[4, \infty) aba^{b} sin(a)\sin (a) \infty α\alpha f1(x)=f^{-1}(x)=

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Problem 307

Find the function value, if possible. q(t)=5t2+6t2q(t)=\frac{5 t^{2}+6}{t^{2}} (a) q(2)q(2) (b) q(0)q(0) (c) q(x)q(-x)

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Problem 308

Suppose f(x)=x1xf(x)=\frac{x-1}{x} and g(x)=11xg(x)=\frac{1}{1-x}
Then (fg)(x)=(f \circ g)(x)= \square , and (gf)(x)=(g \circ f)(x)= \square . Remarkable!

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Problem 309

4. [2.945.88[2.945 .88 Points]
DETAILS MY NOTES SCALCET9 6.XP.1.UOZ. Sketch the region endosed by the given curves. Decide whether to integrate with respect to xx or yy. Draw a typical approximating rectangle. y=x23x,y=2x+6y=x^{2}-3 x, y=2 x+6 fod the wee ef the regian. \square Aned Heip? thanes

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Problem 310

omplete the table. f(x)={36x2,x<6x6,x6f(x)=\left\{\begin{array}{ll} 36-x^{2}, & x<6 \\ x-6, & x \geq 6 \end{array}\right. \begin{tabular}{|l|l|l|l|l|l|} \hlinexx & 4 & 5 & 6 & 7 & 8 \\ \hlinef(x)f(x) & & & & & \\ \hline \end{tabular}

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Problem 311

Note: Triangle may not be drawn to scale. Suppose a=10\mathrm{a}=10 and c=11\mathrm{c}=11. Round answers to one decimal place: sin(A)=cos(A)=tan(A)=sec(A)=csc(A)=cot(A)=\begin{array}{l} \sin (A)=\square \\ \cos (A)=\square \\ \tan (A)=\square \\ \sec (A)=\square \\ \csc (A)=\square \\ \cot (A)=\square \end{array}

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Problem 312

例 2 求函数 y=x3y=x^{3}x=2,Δx=0.02x=2, \Delta x=0.02 时的微分. 解 先求函数在任意点 xx 的微分 dy=(x3)Δx=3x2Δx\mathrm{d} y=\left(x^{3}\right)^{\prime} \Delta x=3 x^{2} \Delta x

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Problem 313

The volume, VV, of a sphere in terms of its radius, rr, is given by V(r)=43πr3V(r)=\frac{4}{3} \pi r^{3}. Express rr as a function of VV, and find the radius of a sphere with volume of 500 cubic feet.
Round your answer for the radius to two decimal places.
Enclose numerators and denominators in parentheses. For example, (ab)/(1+n)(a-b) /(1+n).
Include a multiplication sign between symbols. For example, aπa^{*} \pi. r(V)=r(V)= \square
A sphere with volume 500 cubic feet has radius \square feet.
Show your work and explain, in your own words, how you arrived at your answers.

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Problem 314

- A factory manager, Vin Diesel, knows that on any given day, n employees can fill p(n)=2n8p(n)=2 n-8 orders.
1. How many orders can 10 employees fill in a \cdot day? WARM-UP 2.On Monday, 120 orders need to be filled. How many employees are needed on Monday? 3.On Tuesday, 64 orders need to be filled. How many employees are needed on Tuesday?

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Problem 315

(1) y=3cos(π30x)+8y=3 \cos \left(\frac{\pi}{30} x\right)+8 (3) y=3cos(π30x)+8y=-3 \cos \left(\frac{\pi}{30} x\right)+8 (2) y=3cos(π15x)+5y=3 \cos \left(\frac{\pi}{15} x\right)+5 (4) y=3cos(π15x)+5y=-3 \cos \left(\frac{\pi}{15} x\right)+5

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Problem 316

Use logarithmic differentiation to find the derivative of the function. y==(x5+2)2(x4+4)4y^{\prime}=\square=\left(x^{5}+2\right)^{2}\left(x^{4}+4\right)^{4} Need Help? Watch it

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Problem 317

For a certain drug, the rate of reaction in appropriate unit is given by; R(t)=2t+2R^{\prime}(t)=\frac{2}{\sqrt{t+2}}
Where tt is the time (in hours) after the drug is administered. Find the total reaction to the drug from t=1t=1 to t=6t=6

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Problem 318

Use logarithmic differentiation to find the derivative of the function. y=x2cos(x)y=\begin{array}{c} y=x^{2} \cos (x) \\ y^{\prime}=\square \end{array}

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Problem 319

The image of the point (8,1)(8,1) under a translation is (9,2)(9,2). Find the coordinates of the image of the point (5,5)(5,5) under the same translation.

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Problem 320

Differentiate the function. f(x)=6xln(9x)6xf(x)=\begin{aligned} & f(x)=6 x \ln (9 x)-6 x \\ f^{\prime}(x)= & \end{aligned}

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Problem 321

A table for f(x)f(x) is shown below: \begin{tabular}{|c|c|c|c|c|c|} \hline x\mathbf{x} & -2 & -1 & 0 & 1 & 2 \\ \hline f(x)\mathbf{f}(\mathbf{x}) & 1 & -1 & -2 & 4 & -4 \\ \hline \end{tabular} (3) A table for g(x)g(x) is shown below: \begin{tabular}{|c|r|r|r|r|r|} \hlinexx & -1 & 0 & 1 & 2 & 3 \\ \hlineg(x)g(x) & 1 & -1 & -2 & 4 & -4 \\ \hline \end{tabular}
Based on the table, g(x)=g(x)= f(x)1f(x)-1 f(x)+1f(x)+1 f(x+1)f(x+1) f(x1)f(x-1)
A table for h(x)h(x) is shown below: \begin{tabular}{|c|r|r|r|r|r|} \hline x\mathbf{x} & -2 & -1 & 0 & 1 & 2 \\ \hline h(x)\mathbf{h}(\mathbf{x}) & 0 & -2 & -3 & 3 & -5 \\ \hline \end{tabular}
Based on the table, h(x)=h(x)= f(x)+1f(x)+1 f(x+1)f(x+1) f(x)1f(x)-1 f(x1)f(x-1)

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Problem 322

Use logarithmic differentiation to find the derivative of the function. y=x2cos(x)y=\begin{array}{r} y=x^{2} \cos (x) \\ y^{\prime}=\square \end{array}

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Problem 323

\begin{tabular}{|c|c|c|c|c|c|} \hline x\boldsymbol{x} & -3 & 0 & 3 & 6 & 9 \\ \hline p(x)\boldsymbol{p}(\boldsymbol{x}) & -21 & 0 & 3 & 0 & 11 \\ \hline \end{tabular}
30. The table above gives selected values of the polynomial function f(x)f(x). Assuming all zeroes are given, between what two points on the table will f(x)f(x) have a point of inflection? Justify your answer.
31. The rates of change of the polynomial function g(x)g(x) are increasing for x<3x<-3 and decreasing for x>3x>-3. Use this information to answer the questions below

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Problem 324

例 8 利用微分计算 sin3030\sin 30^{\circ} 30^{\prime} 的近似值. 解 把 303030^{\circ} 30^{\prime} 化为弧度, 得 3030=π6+π36030^{\circ} 30^{\prime}=\frac{\pi}{6}+\frac{\pi}{360}

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Problem 325

Draw the following graph on the interval 330<x<30-330^{\circ}<x<30^{\circ} : y=3cos(x75)y=-3 \cos \left(x-75^{\circ}\right)
Clear All Draw: MM

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Problem 326

f(x)=x3+2x128cos(π2x)+2x2f(x)=\frac{x^{3}+2 x-12}{8 \cos \left(\frac{\pi}{2} x\right)+2 x^{2}}
Let ff be the function defined above. Which of the following conditions explains why ff is not continuous at x=2x=2 ? (A) Neither limx2f(x)\lim _{x \rightarrow 2} f(x) nor f(2)f(2) exists.
B limx2f(x)\lim _{x \rightarrow 2} f(x) exists, but f(2)f(2) does not exist. (C) Both limx2f(x)\lim _{x \rightarrow 2} f(x) and f(2)f(2) exist, but limx2f(x)f(2)\lim _{x \rightarrow 2} f(x) \neq f(2). (D) Both limr?f(x)\lim _{r \rightarrow ?} f(x) and f(2)f(2) exist, and limr ? f(x)=f(2)\lim _{r \rightarrow \text { ? }} f(x)=f(2).

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Problem 327

If f(x)=ln(3x+ln(x))f(x)=\ln (3 x+\ln (x)), find f(1)f^{\prime}(1) f(1)=f^{\prime}(1)= Need Help? Read It

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Problem 328

ddxx2+5x2\frac{d}{d x} \frac{x^{2}+5}{x-2}

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Problem 329

The graph above is a transformation of the function x2x^{2}. Write an formula for the function graphed above:

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Problem 330

Find the Laplace transform of the following functions:
1. f(t)=2t5+4t4+7t3+1f(t)=2 t^{5}+4 t^{4}+7 t^{3}+1 F(s)=F(s)= \square
2. f(t)=7t5+2t4tf(t)=\frac{7 t^{5}+2 t^{4}}{t} F(s)=F(s)= \square

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Problem 331

Find the Laplace transform of the following functions:
1. f(t)=sin(6t)+cos(6t)f(t)=\sin (6 t)+\cos (6 t) F(s)=F(s)=
2. f(t)=(8+9t)2f(t)=(8+9 t)^{2} F(s)=F(s)=

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Problem 332

Let y=f(x)y=f(x) be the piecewise defined function given below. f(x)={x2, if x20, if 2<x<2x2, if x2f(x)=\left\{\begin{array}{ll} -x-2, & \text { if } x \leq-2 \\ 0, & \text { if }-2<x<2 \\ x-2, & \text { if } x \geq 2 \end{array}\right. a. f(3)=f(-3)= \square help (numbers) b. f(2)=f(2)= \square help (numbers) c. For what values of xx is f(x)=0f(x)=0 ? \square help (inequalities) d. Find the domain and range of ff. (You may find it helpful to graph this function on your own paper to find the domain and range.) Your answers must be inequalities (not intervals).
Domain: \square [lnf,lnf][-\operatorname{lnf}, \ln f] help (inequalities)
Range: [0,lnf)[0, \ln f) \square help (inequalities)

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Problem 333

Given f(x)=3x6f(x)=3 \sqrt{x-6} and g(x)=x6g(x)=\sqrt{x-6}, find formulas for f+g,fg,fgf+g, f-g, f g, and f/gf / g plus the domains of each. Enter the domains using interval notation, and use inf for \infty if appropriate. (f+g)(x)=(f+g)(x)= \square Domain == \square (Jg)(x)=(J-g)(x)= \square Domain =[6=[6, Inf )) \square (fg)(x)=3(x6)(f g)(x)=3(x-6) \square \square Domain =[6=[6, Inf )) (fg)(x)=3\left(\frac{f}{g}\right)(x)=3 \square Domain =(6=(6, Inf ))

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Problem 334

oblems 343-4, Use a graphing utility to complete the following. A. Find the real zeros, B. State the value of xx where the local maximum or local minimum occurs, and C. Identify each local extreme value of the function. g(x)=0.25x40.25x32.25x2g(x)=0.25 x^{4}-0.25 x^{3}-2.25 x^{2}
4. h(x)=0.25x5+2.5x30.5x2+4h(x)=-0.25 x^{5}+2.5 x^{3}-0.5 x^{2}+4

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Problem 335

Match the function with its name. f(x)=xf(x)=\llbracket x \rrbracket greatest integer function linear function reciprocal function absolute value function identity function

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Problem 336

Evaluate the function for the given values. k(x)=[2x+1]k(x)=[2 x+1] (a) k(13)k\left(\frac{1}{3}\right) \square (b) k(2.1)k(-2.1) \square (c) k(1.1)k(1.1) \square (d) k(23)k\left(\frac{2}{3}\right) \square

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Problem 337

Determine the domain and range of each of the following: Use interval notation to express your answer, such as (-inf,inf) or (3,5](-3,5] or [10,10][-10,10] \ldots etc (a) f(x)=4+2xf(x)=4+2 x
Domain:
Range: \square \square (b) f(x)=7+5xf(x)=\sqrt{7+5 x} use only simplified exact answers Domain: \square Range: \square (c) f(x)=21+2x+5f(x)=2 \sqrt{1+2 x}+5 use only simplified exact answers Domain: \square Range: \square

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Problem 338

Use the graph of the given function ff to determine the limit at the indicated value of aa, if it exists. (If an answer does not exist, en (i) limf(x)\lim f(x)

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Problem 339

5,6,7\underline{5}, \underline{6}, \underline{7}, and 8\underline{8} Find an equation of the tangent line to the curve at the given point.
5. y=2x25x+1,(3,4)y=2 x^{2}-5 x+1, \quad(3,4)

HIDE ANSWER
Answer: y=7x17y=7 x-17
6. y=x22x3,(1,1)y=x^{2}-2 x^{3}, \quad(1,-1)

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Problem 340

3. Consider the function f(x)=2x2+3x1f(x)=2 x^{2}+3 x-1. Determine: a) f(2x)=2(2x)2+3(2x)1f(2-x)=2(2-x)^{2}+3(2-x)-1 b) f(x2)f\left(x^{2}\right)

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Problem 341

Question 4 of 10 This quiz: 100 This question
Find the following values using a graphing calculator and the TABLE feature set in ASK mode. g(x)=0.05x35.5x20.3xg(x)=0.05 x^{3}-5.5 x^{2}-0.3 x g(3.8)=g(-3.8)= \square (Simplify your answer. Round to the nearest tenth.) g(5.3)=g(5.3)= \square (Simplify your answer. Round to the nearest tenth.) g(11.5)=g(11.5)= \square (Simplify your answer. Round to the nearest tenth.)

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Problem 342

This question: 10 point(s) possible Submit quiz Graph the function. f(x)=12x+8f(x)=\frac{1}{2} x+8
Use the graphing tool on the right to graph the function. \square

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Problem 343

Question Completion Status:
QUESTION 1 Perform the following operation and report your answer with the appropriate number of significant figures / digits of precision. log 100 == ? \square
QUESTION 2 Perform the following operation and report your answer with the appropriate number of significant figures %\% digits of precision. log 56.2 == ? \square
QUESTION 3 Perform the following operation and report your answer with the appropriate number of significant figures / digits of precision. log2.3-\log 2.3 == ? \square

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Problem 344

Given the function f(x)=5x+5f(x)=5 x+5, evaluate and simplify the expressions below. See special instructions on how to enter your answers. f(a)=f(a)= \square f(a+h)=f(a+h)= \square f(a+h)f(a)h=\frac{f(a+h)-f(a)}{h}= \square
Instructions: Simplify answers as much as possible. Expressions such as 4(x+2)4(x+2) and (x+5)2(x+5)^{2} should be expanded. Also collect like terms, so 3x+x3 x+x should be written as 4x4 x.

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Problem 345

Use the graph of the function ff to determine the following limits, if they exist. (If an answer does not exist, enter DNE.) (i) limxf(x)=\lim _{x \rightarrow \infty} f(x)= \qquad limxf(x)=\lim _{x \rightarrow-\infty} f(x)= \square

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Problem 346

Find the cubic polynomial f(x)f(x) such that f(1)=2,f(1)=3,f(1)=12f(-1)=-2, f^{\prime}(-1)=-3, f^{\prime \prime}(-1)=12, and f(1)=12f^{\prime \prime \prime}(-1)=-12. f(x)=f(x)= \square

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Problem 347

Evaluate limxf(x)\lim _{x \rightarrow \infty} f(x) and limxf(x)\lim _{x \rightarrow-\infty} f(x) for the following function. Then give the horizontal asymptote(s) of ff (if any). f(x)=2x3+84x3+64x6+3f(x)=\frac{2 x^{3}+8}{4 x^{3}+\sqrt{64 x^{6}+3}}
Evaluate limxf(x)\lim _{x \rightarrow \infty} f(x). Select the correct choice and, if necessary, fill in the answer box to complete your choice. \qquad A. limxf(x)=\lim _{x \rightarrow \infty} f(x)=\square (Type an integer or a simplified fraction.) B. The limit does not exist and is neither \infty nor -\infty.

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Problem 348

\begin{tabular}{|c|c|c|c|c|c|} \hline teen & 0 & 2 & 4 & 5 & 7 \\ \hline & & & & & \\ \hline (in) & 150 & 190 & 230 & 250 & 290 \\ \hline \end{tabular}

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Problem 349

Differentiate the function. g(x)=2(x)=ln(xe4x)g^{\prime}(x)=\square^{2(x)}=\ln \left(x e^{-4 x}\right)

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Problem 350

g(u)=1/uu2u2g(u)=1 / u-\frac{u^{2}}{u-2}

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Problem 351

10. a) f(x)f(x) is a quadratic function. The graph of f(x)f(x) decreases on the interval (,2)(-\infty,-2) and increases on the interval (2,)(2, \infty). It has a yy-intercept at (0,4)(0,4). What is a possible equation for f(x)f(x) ? b) Is there only one quadratic function, f(x)f(x), that has the characteristics given in part a)? c) If f(x)f(x) is an absolute value function that has the characteristics given in part a), is there only one such function? Explain.

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Problem 352

PREVIUUS AINSWERS PRACTICE AN he Audubon society at Enormous State University (ESU) is planning its annual fund-raising "Eatathon." The society will charge students 90 per serving of pasta. The only expenses the society ww re the cost of the pasta, estimated at 18$18 \$ per serving, and the $360\$ 360 cost of renting the facility for the evening. (a) Write down the associated cost function C(x)C(x) in dollars. C(x)=C(x)= \square Check which variable(s) should be in your answer. Write down the revenue function R(x)R(x) in dollars. R(x)=R(x)= \square Check which variable(s) should be in your answer. Write down the profit function P(x)P(x) in dollars. \square P(x)=P(x)=\square
Check which variable(s) should be in your answer. (b) How many servings of pasta must the Audubon society sell to break even? \square 500 servings (c) What profit (or loss) results from the sale of 1,500 servings of pasta? \square $\$

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Problem 353

My score: 7.58/107.58 / 10 pts ( 75.83%75.83 \% ) Evaluate limxf(x)\lim _{x \rightarrow \infty} f(x) and limxf(x)\lim _{x \rightarrow-\infty} f(x) for the following function. Then give the horizontal asymptote(s) of ff (if any). f(x)=2x3+84x3+64x6+3f(x)=\frac{2 x^{3}+8}{4 x^{3}+\sqrt{64 x^{6}+3}}
Evaluate limxf(x)\lim _{x \rightarrow \infty} f(x). Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. limxf(x)=16\lim _{x \rightarrow \infty} f(x)=\frac{1}{6} (Type an integer or a simplified fraction.) B. The limit does not exist and is neither \infty nor -\infty.
Evaluate limxf(x)\lim _{x \rightarrow-\infty} f(x). Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. limxf(x)=\lim _{x \rightarrow-\infty} f(x)=\square (Type an integer or a simplified fraction.) \square B. The limit does not exist and is neither \infty nor -\infty.

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Problem 354

Netflix Discord Gmail CPI Inflation Calcula... Home - ENGL 1101... HBO GO. It's HBO.... 7.14 Points] DETAILS MY NOTES SCALCET9 6.XP.3.023.
Let RR be the region in the first quadrant bounded by the graphs of y=9xy=\sqrt{9 x} and y=x29y=\frac{x^{2}}{9}. Let VV be the volume of the solid obtained by rotating RR about the yy-axis. Find vv by using washers. v=v=\square

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Problem 355

Given the function f(x)=4(2x)(2+x)23(x1) f(x) = 4(2-x)(2+x)^2 - 3(x-1)
The user took a picture with their phone and the text was extracted above. The user then had a dialogue with an AI Assistant to help clarify the instructions.
Dialogue Transcript:
Hi there! I see you have the function f(x)=4(2x)(2+x)23(x1) f(x) = 4(2-x)(2+x)^2 - 3(x-1) . How can I assist you with this function? Are you looking to find the derivative, solve for x x , find the maximum or minimum, or something else? Let me know so I can help you further! Can you turn into standard form

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Problem 356

Find the limit. (If the limit is infinite, enter ' \infty ' or ' -\infty ', as appropriate. If the limit does not otherwise exist, enter DNE.) limtt+t28tt2\lim _{t \rightarrow \infty} \frac{\sqrt{t}+t^{2}}{8 t-t^{2}}

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Problem 357

Find the inverse function of f(x)=4+x3f(x)=4+\sqrt[3]{x} f1(x)=f^{-1}(x)= \square

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Problem 358

A right triangle has side lengths 8,15 , and 17 as shown below. Use these lengths to find tanA,sinA\tan A, \sin A, and cosA\cos A. tanA=sinA=cosA=\begin{array}{l} \tan A= \\ \sin A= \\ \cos A= \end{array} \square \square

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Problem 359

and 12 , for the given functions ff and gg, find the following: (c) (fg)(x)(f \cdot g)(x) (d) (fg)(x)\left(\frac{f}{g}\right)(x) (b) (fg)(x)(f-g)(x) (g) (fg)(2)(f \cdot g)(2) (h) (fg)(1)\left(\frac{f}{g}\right)(1) (f) (fg)(4)(f-g)(4)
12. f(x)=2x+33x2;g(x)=4x3x2f(x)=\frac{2 x+3}{3 x-2} ; g(x)=\frac{4 x}{3 x-2}

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Problem 360

f(x)=x+3x+10f1(7)=\begin{array}{l}f(x)=\frac{x+3}{x+10} \\ f^{-1}(-7)=\end{array}

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Problem 361

Dianelys was offered a job after college earning a salary of $60,000\$ 60,000. She will get a raise of $2,000\$ 2,000 after each year working for the company. Answer the questions below regarding the relationship between salary and the number of years working at the company.
Answer Attempt 1 out of 2
The independent variable, xx, represents the and the dependent variable is the \qquad , because the depends on the \square \square ・.
A function relating these variables is B(x)=B(x)= \square .
So B(2)=B(2)= \square , meaning 2 \square

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Problem 362

Suppose the derivative of a function is given as dfdx=sin(x)+cos(x)\frac{d f}{d x}=\sin (x)+\cos (x) a. Four students guess what the original function ff is. Check each student's guess by writing its derivative
Alice guesses that f(x)=cos(x)+sin(x)f(x)=\cos (x)+\sin (x).
Check: \square - Bob guesses that f(x)=cos(x)sin(x)f(x)=\cos (x)-\sin (x).
Check \square - Chris guesses that f(x)=cos(x)+sin(x)f(x)=-\cos (x)+\sin (x).
Check: \square - Dani guesses that f(x)=cos(x)sin(x)f(x)=-\cos (x)-\sin (x).
Check: \square b. Which of the four students was correct? Alice Bob Chris Dani

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Problem 363

X Determine if the functions f(x) = -2x-4 and g(x) = 2 are inverses of each other. 2

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Problem 364

Euclidean distance measure is can also defined as \qquad
Select one: a. All of them b. A stage of the KDD process in which new data is added to the existing selection. c. The distance between two points as calculated using the Pythagoras theorem d. The process of finding a solution for a problem simply by enumerating all possible solutions according to some predefined order and then testing them

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Problem 365

Evaluate sec1(2)\sec ^{-1}(-\sqrt{2}). Enter an exact answer in radians.
Provide your answer below: sec1(2)=\sec ^{-1}(-\sqrt{2})= \square rad

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Problem 366

56. What is the pattern rule?
Write an expression to represent the pattern. \begin{tabular}{|c|c|} \hline Input & Output \\ \hline 1 & 2 \\ \hline 2 & 5 \\ \hline 3 & 8 \\ \hline 4 & 11 \\ \hline \end{tabular}

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Problem 367

Find the horizontal and vertical asymptotes of the curve. You may want to use a graphing calculator (or computer) to check your work by graphing the curve and estimating the asymptotes. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.) y=3x2+x1x2+x2x=y=\begin{array}{l} y=\frac{3 x^{2}+x-1}{x^{2}+x-2} \\ x=\square \\ y=\square \end{array} Need Help? Read It

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Problem 368

Entscheiden Sie durch Ankreuzen des zugehörigen Kästchens, welche Aussagen richtig und welche falsch sind. Begründen Sie Ihre Entscheidung bei allen Aussagen in Stichworten. \begin{tabular}{|c|c|c|c|c|c|} \hline & \multicolumn{2}{|l|}{ Die Gerade(n) der Funktionsgraphen zu... } & Richtig & Falsch & Begründung \\ \hline a) & f(x)=12x2f(x)=\frac{1}{2} x-2 & aa und bb sind parallel & \square & \square & \\ \hline b) & f(x)=0,5x1f(x)=-0,5 x-1 & c verläuft durch den & & & \\ \hline c) & f(x)=0,3x+5f(x)=0,3 x+5 & Ursprung & \square & \square & \\ \hline d) & \begin{tabular}{l} f(x)=13xf(x)=\frac{1}{3} x \end{tabular} & \begin{tabular}{l} cc und gg haben dieselbe \\ Steigung \end{tabular} & \square & \square & \\ \hline e) & \begin{tabular}{l} f(x)=12x+3f(x)=\frac{1}{2} x+3 \end{tabular} & \begin{tabular}{l} d verläuft steiler als \\ die Gerade e \end{tabular} & \square & \square & \\ \hline f) & f(x)=5x+1f(x)=5 x+1 & fund gg schneiden sich & & & \\ \hline g) & \begin{tabular}{l} f(x)=13x+1f(x)=\frac{1}{3} x+1 \end{tabular} & auf der yy-Achse & \square & \square & \\ \hline \end{tabular}

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Problem 369

Match each transformation of this function with a graph below. is Tools is Course b¬ 2x2^{-x} a. green (G) c 2x\vee-2^{x} b. red(R)\operatorname{red}(R) a 2x-2^{-x} c. blue (B) Question Help: Video

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Problem 370

Question 3 Le3\mathrm{Le}_{3} [25 marks] Anna's utility function over wine and garbage disposal is UAA=W0.5G0.5\mathrm{UA}_{\mathrm{A}}=\mathrm{W}_{0.5} \mathrm{G} 0.5, and Brewster's utility function is UB=W0.67G0.33\mathrm{U}_{\mathrm{B}}=\mathrm{W}_{0.67} \mathrm{G} 0.33. Anna has 2 bottles of wine and 5 units of garbage disposal services. Brewster has 3 bottles of wine and 3 units of garbage disposal services. (a) In an economy with no exchange, what are the utility levels of Anna and Brewster?

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Problem 371

uestion 15 (1 point) Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a. \begin{tabular}{ll} \hlinexx & H(x)H(x) \\ \hline-1 & 87\frac{8}{7} \\ 0 & 1 \\ 1 & 78\frac{7}{8} \\ 2 & 4964\frac{49}{64} \\ 3 & 343512\frac{343}{512} \\ \hline \end{tabular}

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Problem 372

f1(x)=x12f^{-1}(x)=\sqrt{\frac{x-1}{2}} is the inverse of f(x)=2x21f(x)=2 x^{2}-1. a) True b) False

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Problem 373

Übungsaufgaben 3 Wie lautet die Polynomdarstellung der Parabel, die a) die Abszissenachse in den Punkten Sx1(1/0)S_{x_{1}}(-1 / 0) und Sx2(2/0)S_{x_{2}}(2 / 0) schneidet, nach unten geöffnet und mit dem Faktor 3 in f(x)f(x)-Richtung gedehnt ist?

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Problem 374

corresponding transformations. b) Sketch a graph of y=14[2(x1)]4+2y=\frac{1}{4}[-2(x-1)]^{4}+2.

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Problem 375

Finding the average rate of change of a function
Find the average rate of change of f(x)=2x32x23f(x)=2 x^{3}-2 x^{2}-3 from x=2x=2 to x=3x=3. Simplify your answer as much as possible.

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Problem 376

Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x5,y=1y=x^{5}, y=1, and the yy-axis bout the line y=2y=-2. Enter either an exact answer or an approximate value rounded to at least three decimal places. Volume == \square

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Problem 377

A rod with density ρ(x)=3+sin(x)\rho(x)=3+\sin (x) (in grams per cm ) lies on the x -axis between x=0x=0 and x=5π/6x=5 \pi / 6. Find the mass and center of mass of the rod. (Round each answer to at least 3 decimal places) M=5π2+32+1 grams xˉ=\begin{array}{l} M=\frac{5 \pi}{2}+\frac{\sqrt{3}}{2}+1 \quad \text { grams } \\ \bar{x}=\square \end{array}

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Problem 378

P(x)=x3+6x2+11x+6,x1=3P(x)=x^{3}+6 x^{2}+11 x+6 \quad, x_{1}=-3

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Problem 379

P(x)=2x315x2+27x10x1=5P(x)=2 x^{3}-15 x^{2}+27 x-10 \quad x_{1}=5

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Problem 380

Select the appropriate description of how the graph of each function is derived from the graph of y=x2y=x^{2}. Place the number next to the correct answer. a) y=[13(x)]2\quad y=\left[\frac{1}{3}(x)\right]^{2} \qquad (1) horizontal translation 3 units left (2) vertical translation 3 units up (3) vertical translation 3 units down b) y=(3x)2y=(3 x)^{2} \qquad c) y=x23y=x^{2}-3 \qquad (4) horizontal translation 3 units right and vertical translation 3 units up (5) reflection in xx-axis and vertical translation 3 units up (6) vertical compression by a factor of 13\frac{1}{3} (7) vertical stretching by a factor of 3 d) y=(x3)2y=(x-3)^{2} \qquad (8) horizontal translation 3 units right (9) reflection in xx-axis and horizontal translation 3 units left (10) horizontal stretching by a factor of 3. e) y=(x+3)2\quad y=-(x+3)^{2} \qquad (11) horizontal compression by a factor of 13\frac{1}{3} f) y=x2+3y=-x^{2}+3 \qquad

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Problem 381

me: \qquad plication Date: \qquad
1. Determine the inverse of following relation and state the domain and range of f(x)f(x) as well as its inverse. Show all work. Is the inverse a function? f(x)=(x4)2+6f(x)=(x-4)^{2}+6

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Problem 382

Determine the inverse of the function given in the graph. The points are (3,4)(-3, 4), (1,1)(1, -1), (2,3)(2, 3), (4,3)(4, 3).

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Problem 383

Find the exact value of the expression. sec[sin1(2107)]\sec \left[\sin ^{-1}\left(\frac{2 \sqrt{10}}{7}\right)\right]
Select the correct choice and fill in any answer boxes in your choice below. A. sec[sin1(2107)]=\sec \left[\sin ^{-1}\left(\frac{2 \sqrt{10}}{7}\right)\right]= \square (Simplify your answer, including any radicals. Use integers or fractions for any number B. There is no solution.

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Problem 384

2. Richard Petty has a utility function u(x,y,z)=xy(1+z)u(x, y, z)=x y(1+z) where xx is food, yy is clothing, and zz is automobiles. The price of a unit of food is $1\$ 1, a unit of clothes is $2\$ 2, and a 1 unit of cars is $2000\$ 2000. Cars must be bought in discrete units. Richard has an income of $9000\$ 9000. Calculate the bundle of goods that maximizes Richard's utility.

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Problem 385

[6] 2. Given the equation f(x)=32(x1)+4\quad f(x)=-3|2(x-1)|+4 a) State the parent function: \qquad c) Graph the function, showing the original an graph. Label all point final clearly b) Show transformation of 5 points of your choice:

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Problem 386

[3] 3. Given f(x)=3k2xf(x)=3 k-2 x, find the value of kk if f1(5)=2f^{-1}(5)=-2.

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Problem 387

\qquad
4. Find the constant aa that makes f(x)f(x) a continuous functions. A. 0 B. 3 f(x)={x22x+3,x1ax2+4x2,x>1f(x)=\left\{\begin{array}{cc} x^{2}-2 x+3, & x \leq 1 \\ a x^{2}+4 x-2, & x>1 \end{array}\right. C. 2 D. -2

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Problem 388

The table represents a linear function. The rate of change between the points (5,10)(-5,10) and (4,5)(-4,5) is -5 . What is the rate of change between the points (3,0)(-3,0) and (2,5)(-2,-5) ? \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline-5 & 10 \\ \hline-4 & 5 \\ \hline-3 & 0 \\ \hline-2 & -5 \\ \hline \hline \end{tabular} 5-5 15-\frac{1}{5} 15\frac{1}{5} 5 Mark this and return Save and Exit Next Submit

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Problem 389

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 1 & -9 \\ \hline 2 & -13 \\ \hline 3 & -17 \\ \hline 4 & -21 \\ \hline \end{tabular}
Answer \square Submit Answer

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Problem 390

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 1 & -3 \\ \hline 2 & -2 \\ \hline 3 & -1 \\ \hline 4 & 0 \\ \hline \end{tabular}
Answer \square Submit Answer

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Problem 391

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline-3 & 17 \\ \hline 1 & -3 \\ \hline 5 & -23 \\ \hline 9 & -43 \\ \hline \end{tabular}
Answer \square Submit Answer Forixey Policyl Permes of Sentice

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Problem 392

The graph of y=f(x)y=f(x) is the solid black graph below. Which function represents the dotted graph?
Answer Attempt 1 out of 3 y=f(x)2y=-f(x)-2 y=f(x+2)y=-f(x+2) Submit Answer y=f(x2)y=-f(x-2) y=f(x)+2y=-f(x)+2

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Problem 393

The graph of y=f(x)y=f(x) is the solid black graph below. Which function represents the dotted graph?
Answer Attempt 1 out of 3 y=f(x+4)y=-f(x+4) y=f(x)+4y=-f(x)+4 y=f(x)4y=-f(x)-4 y=f(x4)y=-f(x-4)

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Problem 394

1) Find the slope of the line that passes through the following two points: (1,3)3(5,5)(-1,3) \quad 3(5,5)

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Problem 395

Find the derivative of f(x)=7x2+2xf(x)=7 x^{2}+2 x

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Problem 396

4. The flight of an aircraft from Toronto to Montréal can be modelled by the relation h=2.5t2+200th=-2.5 t^{2}+200 t, where tt is the time, in minutes, and hh is the height, in metres. a) Graph the relation. b) How long does it take to fly from Toronto to Montréal? c) What is the maximum height of the aircraft? At what time does the aircraft reach this height? 4.3 Investigate Transformations of Quadratics, pages 174-179, and 4.4 Graph y=a(xh)2+ky=a(x-h)^{2}+k, pages 180188180-188
5 sketch the graph of each parabola. Describe

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Problem 397

omplete the square to re-write the quadratic function in vertex form: y=x2+8x4y=x^{2}+8 x-4

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Problem 398

2) Does this data represent an exponential function? * 1 point
Does this data represent an EXPONENTIAL FUNCTION? \begin{tabular}{|c|c|c|c|c|c|c|} \hline X & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline y & 4096 & 1024 & 256 & 64 & 16 & 4 \\ \hline \end{tabular} Yes No

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Problem 399

What is the domain of y=log5xy=\log _{5} x ? all real numbers less than 0 all real numbers greater than 0 all real numbers not equal to 0 all real numbers

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Problem 400

Use Descartes' Rule to determine the possible number of positive and negative real zeros. Then graph to confirm which of those possibilities is the actual combination.  Use Descartes’ Rule to determine the possible  number of positive and negative real zeros. Then  graph to confirm which of those possibilities is the  actual combination. f(x)=x32x2+x1 The number of possible positive real zeros is  (check all that apply) 0.12 The number of possible negative real zeros is  (check all that apply) 0.1008\begin{array}{l} \text { Use Descartes' Rule to determine the possible } \\ \text { number of positive and negative real zeros. Then } \\ \text { graph to confirm which of those possibilities is the } \\ \text { actual combination. } \\ f(x)=x^{3}-2 x^{2}+x-1 \\ \text { The number of possible positive real zeros is } \\ \text { (check all that apply) } 0.1 \square 2 \text {. } \\ \text { The number of possible negative real zeros is } \\ \text { (check all that apply) } 0.100^{8} \text {. } \end{array}
The number of possible positive real zeros is (check all that apply) \square 0 1 \square 2 \square 3 \square 8.
The number of possible negative real zeros is (check all that apply) \qquad 0 \qquad 1 2 3 o8o^{8} . .  Use Descartes’ Rule to determine the possible  number of positive and negative real zeros. Then  graph to confirm which of those possibilities is the  actual combination. f(x)=x32x2+x1 The number of possible positive real zeros is  (check all that apply) 0123 The number of possible negative real zeros is  (check all that apply) 0.102\begin{array}{l} \begin{array}{l} \text { Use Descartes' Rule to determine the possible } \\ \text { number of positive and negative real zeros. Then } \\ \text { graph to confirm which of those possibilities is the } \\ \text { actual combination. } \\ f(x)=x^{3}-2 x^{2}+x-1 \\ \text { The number of possible positive real zeros is } \\ \text { (check all that apply) } 0 \checkmark 1 \square 2 \square 3 \text {. } \\ \text { The number of possible negative real zeros is } \\ \text { (check all that apply) } 0.102 \text {. } \end{array} \end{array} \qquad \qquad Part 2  Part 2\text { Part } 2 \qquad \qquad \qquad - \square . \qquad

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