Calculus Examples

$lim_{x \to - \infty} \frac{e^{x} + e^{- x}}{2}$

Step 1

Consider the limit with the constant multiple $\frac{1}{2}$ removed.

$lim_{x \to - \infty} e^{x} + e^{- x}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- \infty$ .

$lim_{x \to - \infty} e^{x} + lim_{x \to - \infty} e^{- x}$

Step 3

Since the exponent $x$ approaches $- \infty$ , the quantity $e^{x}$ approaches $0$ .

$0 + lim_{x \to - \infty} e^{- x}$

Step 4

Since the exponent $- x$ approaches $\infty$ , the quantity $e^{- x}$ approaches $\infty$ .

$0 + \infty$

Step 5

Add $0$ and $\infty$ .

$\infty$