Question

If ​f(1)equals​5, must ModifyingBelow lim With x right arrow 1 f (x )​exist? If it​ does, then must ModifyingBelow lim With x right arrow 1 f (x )equals​5? Can we conclude anything about ModifyingBelow lim With x right arrow 1 f (x )​?

Answer 1

Answer:

Answer to all three points is NO.

Step-by-step explanation:

Case 1:

$\lim_{x \to \>>1} f(x)= 1$

Answer : NO, It is important to note that the even if function is not defined, the limit of function can exist and it doesn't mean that f(x) must necessarily be defined at x = 1

Case 2:

Answer : No, because it could be a piece wise function even if f is defined, where f(1) might have different values while approaching from right and left side of limits.

Case 3:

Answer: No, value of f(1) can not be concluded