Q. 61 - 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. 

$\underset{x\to \raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\lim }\tan x$

Step-by-Step Solution

Answer

The graph for given limit

The given limit expression does not have any value 

Step 1. Given information

The given limit $\underset{x\to \raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\lim }\tan x$

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 the left of $x\to \frac{\mathrm{\pi }}{2}$ the value of the function goes to $\infty$.And for the right of $x\to \frac{\mathrm{\pi }}{2}$ the value goes to $-\infty$

Therefore,the limit expression does not have any value