Suppose that a function f(x) is defined for all real values of x in [-1,1]. Can

Question

Suppose that a function f(x) is defined for all real values of x in [-1,1]. Can anything be said about the existence of lim f(x)? Give reasons for your answer. x-+0 0 A. At x=0, lim f(x) does not exist because it is likely that the function oscillates or jumps at that point. O B. At x = 0, lim f(x) must exist because the function is defined at every point in the interval [-1,1] C. Nothing can be said about the existence of the limit. Even though the function is defined at every point in the interval [-1,11, there may be a jump or an oscillation at x = 0.

Explanation / Answer

Although the limit is defined at every point in the interval [-1,1] but there might be a jump at any point where in between the interval.

Answer - option C

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