contestada

Suppose that for a function f,f(2) is not defined. Also suppose that limx→2−f(x)=7 and limx→2+f(x)=7. Which, if any, of the following statements is false? a) limx→2f(x)=7 b) f has jump discontinuity at x = 2 c) If we re-define f so that f(2) = 7 then the new function will be continuous at x = 2 d) f has removable discontinuity at x = 2 e) All of the above statements are true.

Respuesta :

All of the statements are true.

If the limit of a function f(x) at x = a is exist .

            [tex]\lim_{x \to a+} f(x)= \lim_{x \to a-} f(x)=f(a)[/tex]

Given that,

          [tex]\lim_{x \to 2-} f(x)= \lim_{x \to 2+} f(x)=7[/tex]

But f(2) is not defined.

It means that function f(x) has jump discontinuity at x = 2

A removable discontinuity is a point on the graph that is undefined or does not fit the rest of the graph.

So that, Function f(x) has removable discontinuity at x = 2

Learn more:

https://brainly.com/question/20543024

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