Question

Review the graph of function f(x).

what are lim x-> 0 f(x) and lim x-> 0 f(x) if they exist

Answer 1

The two limits when x tends to zero are:

$\lim_{x \to \ 0^-} f(x) = 1\\\\ \lim_{x \to \ 0^+} f(x) = 0$

How to get the limits when x tends to zero?

Notice that we have a jump at x = 0.

Then we can take two limits, one going from the negative side (where we will go along the blue line)

And other from the positive side (where we go along the orange line).

We will get:

$\lim_{x \to \ 0^-} f(x) = 1\\\\ \lim_{x \to \ 0^+} f(x) = 0$

Notice that the two limits are different, that means that the function is not a continuous function.

If you want to learn more about limits:

https://brainly.com/question/5313449

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