Q. 60 - 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. 

$\underset{x\to -\infty }{\lim }\left(3e^{4x}+1\right)$

Step-by-Step Solution

Answer

Graph for the given limit

The limit expression has the value of $\underset{x\to -\infty }{\lim }\left(3e^{4x}+1\right)=1$

Step 1. Given information

The given limit $\underset{x\to -\infty }{\lim }\left(3e^{4x}+1\right)$

Step 2. Sketch graphs by hand and use them to make approximations for the limit

The graph is drawn as below:

From the graph,we see that for $x\to -\infty$ the function has a value of $f\left(x\right)=1$

Therefore,the limit expression has the value of  $\underset{x\to -\infty }{\lim }\left(3e^{4x}+1\right)=1$