QuestionFind the limit as $x$ approaches $\pi$ for $\sqrt{3+\cos 4x}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to find the limit of the function $\sqrt{3+\cos4x}$ as $x$ approaches $\pi$ . . We will use the limit properties and the knowledge of trigonometric functions to solve this problem.

STEP 2

First, we need to substitute $x = \pi$ into the function, if the function is continuous at $x = \pi$ . $\lim{x \rightarrow \pi} \sqrt{+\cos4x} = \sqrt{+\cos4\pi}$

STEP 3

Now, we need to calculate the cosine of $\pi$ . $\cos\pi =1$

STEP 4

Substitute the value of $\cos4\pi$ back into the function.
$\sqrt{3+1} = \sqrt{4}$

STEP 5

Finally, calculate the square root of4.
$\sqrt{4} =2$ So, the limit of the function $\sqrt{3+\cos4x}$ as $x$ approaches $\pi$ is2.

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QuestionFind the limit as $x$ approaches $\pi$ for $\sqrt{3+\cos 4x}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to find the limit of the function $\sqrt{3+\cos4x}$ as $x$ approaches $\pi$ . . We will use the limit properties and the knowledge of trigonometric functions to solve this problem.

STEP 2

First, we need to substitute $x = \pi$ into the function, if the function is continuous at $x = \pi$ . $\lim{x \rightarrow \pi} \sqrt{+\cos4x} = \sqrt{+\cos4\pi}$

STEP 3

Now, we need to calculate the cosine of $\pi$ . $\cos\pi =1$

STEP 4

Substitute the value of $\cos4\pi$ back into the function.
$\sqrt{3+1} = \sqrt{4}$

STEP 5

Finally, calculate the square root of4.
$\sqrt{4} =2$ So, the limit of the function $\sqrt{3+\cos4x}$ as $x$ approaches $\pi$ is2.

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QuestionFind the limit as xxx approaches π\piπ for 3+cos⁡4x\sqrt{3+\cos 4x}3+cos4x​.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the limit of the function 3+cos⁡4x\sqrt{3+\cos4x}3+cos4x​ as xxx approaches π\piπ. . We will use the limit properties and the knowledge of trigonometric functions to solve this problem.

STEP 2

First, we need to substitute x=πx = \pix=π into the function, if the function is continuous at x=πx = \pix=π.lim⁡x→π+cos⁡4x=+cos⁡4π\lim{x \rightarrow \pi} \sqrt{+\cos4x} = \sqrt{+\cos4\pi}limx→π+cos4x​=+cos4π​

STEP 3

Now, we need to calculate the cosine of π\piπ.cos⁡π=1\cos\pi =1cosπ=1

STEP 4

Substitute the value of cos⁡4π\cos4\picos4π back into the function.3+1=4\sqrt{3+1} = \sqrt{4}3+1​=4​

STEP 5

Finally, calculate the square root of4.4=2\sqrt{4} =24​=2So, the limit of the function 3+cos⁡4x\sqrt{3+\cos4x}3+cos4x​ as xxx approaches π\piπ is2.

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QuestionFind the limit as $x$ approaches $\pi$ for $\sqrt{3+\cos 4x}$ .

Assumptions1. We are asked to find the limit of the function $\sqrt{3+\cos4x}$ as $x$ approaches $\pi$ . . We will use the limit properties and the knowledge of trigonometric functions to solve this problem.

First, we need to substitute $x = \pi$ into the function, if the function is continuous at $x = \pi$ . $\lim{x \rightarrow \pi} \sqrt{+\cos4x} = \sqrt{+\cos4\pi}$

Now, we need to calculate the cosine of $\pi$ . $\cos\pi =1$

Substitute the value of $\cos4\pi$ back into the function.
$\sqrt{3+1} = \sqrt{4}$

Finally, calculate the square root of4.
$\sqrt{4} =2$ So, the limit of the function $\sqrt{3+\cos4x}$ as $x$ approaches $\pi$ is2.