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

$\infty$ .

$\infty$