Calculus Examples

$lim_{x \to 8} \arctan (\frac{\sqrt{3} x + 7}{x + 1})$

Step 1

Simplify the answer.

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Step 1.1

Move $8$ to the left of $\sqrt{3}$ .

$\frac{8 \sqrt{3} + 7}{8 + 1}$

Step 1.2

Add $8$ and $1$ .

$\frac{8 \sqrt{3} + 7}{9}$

Step 2

Substitute $t$ for $\frac{\sqrt{3} x + 7}{x + 1}$ and let $t$ approach $\frac{8 \sqrt{3} + 7}{9}$ since $lim_{x \to 8} \frac{\sqrt{3} x + 7}{x + 1} = \frac{8 \sqrt{3} + 7}{9}$ .

$lim_{t \to \frac{8 \sqrt{3} + 7}{9}} \arctan (t)$

Step 3

Evaluate the limits by plugging in $\frac{8 \sqrt{3} + 7}{9}$ for all occurrences of $t$ .

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Step 3.1

Simplify the answer.

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Step 3.1.1

Move $8$ to the left of $\sqrt{3}$ .

$\arctan (\frac{8 \sqrt{3} + 7}{8 + 1})$

Step 3.1.2

Add $8$ and $1$ .

$\arctan (\frac{8 \sqrt{3} + 7}{9})$

Step 3.2

Evaluate $\arctan (\frac{8 \sqrt{3} + 7}{9})$ .

$1.16341441$