Explain what it means to say that lim x 1 f ( x ) = 9 and lim x 1 + f ( x ) = 7.

Question

Explain what it means to say that

lim x 1f(x) = 9      and      lim x 1+f(x) = 7.

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In this situation is it possible that lim x 1 f(x) exists? which multiple choice options is correct 1-4

1) Yes, the limit can exist because the left- and right hand limits are both 1.

2) Yes, the limit can exist even though the left- and right-hand limits are different.     

3) No, the limit does not exist because the left- and right hand limits are both 1.

4) No, the limit does not exist because the left- and right-hand limits are different.

Explanation / Answer

Solution :- We have given that

lim x 1 f(x) = 9      and      lim x 1+ f(x) = 7.

since we know that the limit of a function f(x) at x=a exist if right hand lim x a+ f(x) = left hand limit lim x a f(x) = f(a) .

Here the left hand limit of f(x) does not equal to right hand limit at x=1 .

Hence No, the limit does not exist because the left- and right-hand limits are different.

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