QuestionFind the limit: $\lim _{x \rightarrow 4} \sqrt{1+2 x}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to find the limit of the function $\sqrt{1+x}$ as $x$ approaches4. . We will use the direct substitution method to find the limit.

STEP 2

The direct substitution method involves substituting the value that $x$ is approaching into the function.
$\lim{x \rightarrow4} \sqrt{1+2 x} = \sqrt{1+2(4)}$

STEP 3

Now, simplify the expression inside the square root.
$\sqrt{1+2()} = \sqrt{1+8}$

STEP 4

Further simplify the expression inside the square root.
$\sqrt{1+8} = \sqrt{9}$

STEP 5

Finally, calculate the square root of9.
$\sqrt{9} =3$ So, the limit of the function $\sqrt{1+2x}$ as $x$ approaches4 is3.

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QuestionFind the limit: $\lim _{x \rightarrow 4} \sqrt{1+2 x}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to find the limit of the function $\sqrt{1+x}$ as $x$ approaches4. . We will use the direct substitution method to find the limit.

STEP 2

The direct substitution method involves substituting the value that $x$ is approaching into the function.
$\lim{x \rightarrow4} \sqrt{1+2 x} = \sqrt{1+2(4)}$

STEP 3

Now, simplify the expression inside the square root.
$\sqrt{1+2()} = \sqrt{1+8}$

STEP 4

Further simplify the expression inside the square root.
$\sqrt{1+8} = \sqrt{9}$

STEP 5

Finally, calculate the square root of9.
$\sqrt{9} =3$ So, the limit of the function $\sqrt{1+2x}$ as $x$ approaches4 is3.

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QuestionFind the limit: lim⁡x→41+2x\lim _{x \rightarrow 4} \sqrt{1+2 x}limx→4​1+2x​.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the limit of the function 1+x\sqrt{1+x}1+x​ as xxx approaches4. . We will use the direct substitution method to find the limit.

STEP 2

The direct substitution method involves substituting the value that xxx is approaching into the function.lim⁡x→41+2x=1+2(4)\lim{x \rightarrow4} \sqrt{1+2 x} = \sqrt{1+2(4)}limx→41+2x​=1+2(4)​

STEP 3

Now, simplify the expression inside the square root.1+2()=1+8\sqrt{1+2()} = \sqrt{1+8}1+2()​=1+8​

STEP 4

Further simplify the expression inside the square root.1+8=9\sqrt{1+8} = \sqrt{9}1+8​=9​

STEP 5

Finally, calculate the square root of9.9=3\sqrt{9} =39​=3So, the limit of the function 1+2x\sqrt{1+2x}1+2x​ as xxx approaches4 is3.

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QuestionFind the limit: $\lim _{x \rightarrow 4} \sqrt{1+2 x}$ .

Assumptions1. We are asked to find the limit of the function $\sqrt{1+x}$ as $x$ approaches4. . We will use the direct substitution method to find the limit.

The direct substitution method involves substituting the value that $x$ is approaching into the function.
$\lim{x \rightarrow4} \sqrt{1+2 x} = \sqrt{1+2(4)}$

Now, simplify the expression inside the square root.
$\sqrt{1+2()} = \sqrt{1+8}$

Further simplify the expression inside the square root.
$\sqrt{1+8} = \sqrt{9}$

Finally, calculate the square root of9.
$\sqrt{9} =3$ So, the limit of the function $\sqrt{1+2x}$ as $x$ approaches4 is3.