Mathematics: 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.

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Determine if the given function can be extended - id7061390, wakandafoodyoup9ioz4

beaniewastaken

30.01.2022

Complete Question

The complete question is shown on the first uploaded image

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

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