Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

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

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

Step 1.2

Move the limit into the exponent.

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

Step 1.3

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

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

Step 2

Since its numerator approaches a real number while its denominator is unbounded, the fraction $\frac{1}{x}$ approaches $0$ .

$- e^{- 0}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $- 1$ by $0$ .

$- e^{0}$

Step 3.2

Anything raised to $0$ is $1$ .

$- 1 \cdot 1$

Step 3.3

Multiply $- 1$ by $1$ .

$- 1$