Question

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

${\displaystyle \underset{x\to 3}{lim}\frac{1}{x-3}}$

Answer 1

To find ${\displaystyle \underset{x\to 3}{lim}\frac{1}{x-3}}$

y = f(x) = ${\displaystyle \frac{1}{x-3}}$

From the graph the value of the function at x = 3 the curve does not meet the line x = 3

∴ The value of the function is not defined at the point x = 3.

Hence ${\displaystyle \underset{x\to 3}{lim}\frac{1}{x-3}}$ does not exist at x = 3.