Calculus Examples

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

Step 1

Move the limit into the exponent.

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

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

Anything raised to $0$ is $1$ .

$1$