Question

In exercise problems 7 – 15, use the graph to find the limits (if it exists). If the limit does not exist, explain why?

${\displaystyle \underset{x\to \frac{x}{2}}{lim}\tan x}$

Answer 1

${\displaystyle \underset{x\to \frac{x}{2}}{lim}\tan x}$

y = f(x) = sec x

From the graph at x = ${\displaystyle \frac{\pi }{2}}$, the curve does not intersect the line x = ${\displaystyle \frac{\pi }{2}}$

At x = ${\displaystyle \frac{\pi }{2}}$, he value of the function y = f(x) does not exist.

Hence ${\displaystyle \underset{x\to \frac{x}{2}}{lim}\tan x}$ does not exist.