Calculus Examples

$lim_{x \to 8} \arctan (\frac{x}{2})$

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Factor $2$ out of $8$ .

$\frac{1}{2} \cdot (2 (4))$

Step 1.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 4)$

Step 1.3

Rewrite the expression.

$4$

Step 2

Substitute $t$ for $\frac{x}{2}$ and let $t$ approach $4$ since $lim_{x \to 8} \frac{x}{2} = 4$ .

$lim_{t \to 4} \arctan (t)$

Step 3

Evaluate the limits by plugging in $4$ for all occurrences of $t$ .

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Factor $2$ out of $8$ .

$\arctan (\frac{1}{2} \cdot (2 (4)))$

Step 3.1.2

Cancel the common factor.

$\arctan (\frac{1}{2} \cdot (2 \cdot 4))$

Step 3.1.3

Rewrite the expression.

$\arctan (4)$

Step 3.2

Evaluate $\arctan (4)$ .

$1.32581766$