Suppose that a function f(x) is defined for all real values of x except at x = c

Question

Suppose that a function f(x) is defined for all real values of x except at x = c. Can anything be said about the existence of lim_x rightarrow c f(x)? Give reasons for your answer. Nothing can be said about the existence of the limit. The function might approach the same value from both sides, or it might jump or oscillate as x rightarrow c. At x = c, lim_x rightarrow c f(x) exists, and its value is the average of the values obtained as x approaches c from the right and from the left. At x = c, lim_x rightarrow c f(x) does not exist because the function is undefined at the point x = c. At x = c, lim_x rightarrow c f(x) does not exist because it is likely that the function oscillates or jumps at that point.

Explanation / Answer

option: A

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