Q. 59 - Calculus

Question

Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits 

$\underset{x\to \infty }{\lim }\left(1-e^{-x}\right)$

Step-by-Step Solution

Answer

The value is $\underset{x\to \infty }{\lim }\left(1-e^{-x}\right)=1$ and graph is,

Step 1. Given informaton.

The given function is $\underset{x\to \infty }{\lim }\left(1-e^{-x}\right).$

Step 2. Graph of the function.

The graph of the function is,

$$\begin{gathered} As x\to \infty , f\left(x\right)\to 1. \\ Therefore, \\ \underset{x\to \infty }{\lim }\left(1-e^{-x}\right)=1 \end{gathered}$$