Question

use a graph to find the following limit. \\(\lim_{x \to \infty} e^x\\) \\(\lim_{x \to \infty} e^x = \boxed{\infty}\\) (simplify your answer.)

Explanation:

Step1: Recall the graph of \( e^x \)

The function \( y = e^x \) is an exponential growth function. Its graph rises rapidly as \( x \) increases.

Step2: Analyze the limit as \( x \to \infty \)

As \( x \) approaches positive infinity, the value of \( e^x \) grows without bound. This means the function \( e^x \) does not approach a finite number but instead goes to infinity.

Answer:

\(\infty\)