Question

Determine if the given function can be extended to a continuous function at xequals0. If​ so, approximate the extended​ function's value at xequals0. If​ not, determine whether the function can be continuously extended from the left or from the right and provide the values of the extended functions at xequals0.

Answer 1

Complete Question

The  complete question is shown on the first uploaded image

Answer:

The correct option is  A

Step-by-step explanation:

Now  from the question we are given the function

        $f(x) = \frac{10^{2 x} -4}{x}$

Now  as  $\lim_{x \to 0} [f(x) ] = \frac{10^{2*0} -4 }{0}$

       =>    $\lim_{x \to 0} [f(x) ] = - \infty$

This  implies that as $x\to 0$ the function $f(x) \to -\infty$ which means that at  x = 0  the function is not continuous