Calculus Examples

$lim_{x \to - 8} \arctan (e^{x} - 1)$

Step 1

Simplify each term.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{e^{8}} - 1 \cdot 1$

Step 1.2

Multiply $- 1$ by $1$ .

$\frac{1}{e^{8}} - 1$

Step 2

Substitute $t$ for $e^{x} - 1$ and let $t$ approach $\frac{1}{e^{8}} - 1$ since $lim_{x \to - 8} e^{x} - 1 = \frac{1}{e^{8}} - 1$ .

$lim_{t \to \frac{1}{e^{8}} - 1} \arctan (t)$

Step 3

Evaluate the limits by plugging in $\frac{1}{e^{8}} - 1$ for all occurrences of $t$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\arctan (\frac{1}{e^{8}} - 1 \cdot 1)$

Step 3.1.2

Multiply $- 1$ by $1$ .

$\arctan (\frac{1}{e^{8}} - 1)$

Step 3.2

Evaluate $\arctan (\frac{1}{e^{8}} - 1)$ .

$- 0.7852304$