Calculus Examples

$\frac{lim_{x \to 8} e^{- x}}{\ln (1 + 4 e^{- x})}$

Step 1

Move the limit into the exponent.

$\frac{e^{lim_{x \to 8} - x}}{\ln (1 + 4 e^{- x})}$

Step 2

Move the term $- 1$ outside of the limit because it is constant with respect to $x$ .

$\frac{e^{- lim_{x \to 8} x}}{\ln (1 + 4 e^{- x})}$

Step 3

Simplify terms.

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Step 3.1

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$\frac{e^{- 8}}{\ln (1 + 4 e^{- x})}$

Step 3.2

Simplify the answer.

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Step 3.2.1

Move $e^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{\ln (1 + 4 e^{- x}) e^{8}}$

Step 3.2.2

Reorder factors in $\frac{1}{\ln (1 + 4 e^{- x}) e^{8}}$ .

$\frac{1}{e^{8} \ln (1 + 4 e^{- x})}$