Find false statement about f(x) with f′(x)=x2−2x+1. Options: a) f(x) increases always, b) f(x) has horizontal inflection at x=1, c) f(x) is concave up always, d) f(x) is concave up for x>1.
Find the approximate percent of adult height attained by girls at age 5 using the function f(x)=62+35log(x−4), where x represents the girl's age (from 5 to 15) and f(x) represents the percent of her adult height.
Evaluate the integral ∫(x+1)(x2+x)9dx. Consider the partial fraction decomposition (x+1)(x2+x)9=x9−(x+1)29x. Identify any errors in the work shown.
Earthquake intensity is 10M=I0I, where M is magnitude, I is intensity, and I0 is reference intensity. Earthquake A is 225 times as intense as B, and B has magnitude 3.8. Which equation determines magnitude m of earthquake A?
m=log225+3.8
Evaluate the absolute value of the integral of ∣x2−4∣ from -2 to 2, and the absolute value of the integral of x2−4 from -2 to 2. Are the results the same?
Determine the credit card balance after 6 months using the exponential function f(x)=800(1+0.122)x, where x represents the number of months. Round the answer to the nearest cent.
Determine the function describing a toy rocket's height, its maximum height and time, the time interval it's above 268 feet, and when it hits the ground, given an initial velocity of 180 feet/second from a 145-foot building.
Graph y=2cos2(x) and y=2e−x+2x−2 on [0,2π). Find the intersection points and their coordinates to 4 decimal places. If no solution, enter "NO SOLUTION".
Find the correct statement about the exponential function k(x)=5(72)x: A) Increasing, concave up B) Increasing, concave down C) Decreasing, concave up D) Decreasing, concave down.
(A) Find the exact cost of producing the 71st food processor, given C(x)=1900+40x−0.2x2.
(B) Use the marginal cost to approximate the cost of producing the 71st food processor.
(A) The exact cost of producing the 71st food processor is $2,662.
(B) Using the marginal cost, the approximate cost of producing the 71st food processor is $2,660.
Find the change in x and y when y varies at a constant rate of 4 with respect to x, for the given ranges of x. a. If x varies from x=3.7 to x=8.8, then:
i. The change in x is Δx=5.1
ii. The corresponding change in y is Δy=20.4 b. If x varies from x=2 to x=−7, then:
i. The change in x is Δx=−9
ii. The corresponding change in y is Δy=−36
The velocity needed to remove a foreign object from a 26-mm radius windpipe is V(r)=k(26r2−r3), where 0≤r≤26. The object that needs maximum velocity to remove has a radius of 13 mm.
Étudier la fonction g(x)=1+xlnx définie sur ]0;+∞[. Résoudre g(x)=0 et déterminer le signe de g. Étudier la famille de fonctions hn(x)=x2−n+nlnx avec n∈N∗, trouver leurs zéros et leur signe. Étudier la famille de fonctions fn(x)=x−n−xnlnx, leurs asymptotes, variations et minimum. Calculer une primitive de fn.
Rewrite f(x)=logax to show −f(x)=log1/ax. Let y=f(x), then y=logax. Rewrite the left side of the equation using logarithm properties to show −f(x)=log1/ax.
Find the volume of a solid with a triangular base and semicircular cross-sections perpendicular to the x-axis. The triangle has vertices at (0,0),(2,0),(0,2). Select one:
V=∫028π(2−x)2dxV=∫024π(x−2)2dx
Find the power series for the indefinite integral ∫7xe8x−1dx, and give the first 5 nonzero terms. f(x)=C+78x+7⋅2!64x2+7⋅3!512x3+7⋅4!4096x4+7⋅5!32768x5+⋯
Identify local/absolute extrema and inflection points of y=(x−3)3+4. Find local max/min points.
A. Local max point(s): (3,4)
B. Local min point(s): (3,4)
Determine weekly sales decline after ad campaign using y=18,000(8−0.05x), where x is weeks since end. Find sales at end and 2 weeks later, and whether sales reach $0.