Calculus Examples

$lim_{x \to - 1} e^{\frac{1}{x}}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

$e^{lim_{x \to - 1} \frac{1}{x}}$

Step 1.2

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $- 1$ .

$e^{\frac{lim_{x \to - 1} 1}{lim_{x \to - 1} x}}$

Step 1.3

Evaluate the limit of $1$ which is constant as $x$ approaches $- 1$ .

$e^{\frac{1}{lim_{x \to - 1} x}}$

Step 2

Evaluate the limit of $x$ by plugging in $- 1$ for $x$ .

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

Step 3

Simplify the answer.

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Step 3.1

Divide $1$ by $- 1$ .

$e^{- 1}$

Step 3.2

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

$\frac{1}{e}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{e}$

Decimal Form:

$0.36787944 \dots$