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Consider the following statements : 1....

Consider the following statements :
1. If `lim_(xtoa) f(x) and lim_(xtoa) g(x)` both exist, then `lim_(xtoa) {f(x)g(x)}` exists.
2. If `lim_(xtoa) {f(x)g(x)}` exists, then both `lim_(xtoa) f(x) and lim_(xtoa) g(x)` must exist.
Which of the above statements is /are correct?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

Text Solution

Verified by Experts

The correct Answer is:
A
If `underset(xtoa)limf(x)andunderset(xtoa)limg(x)` both exists, then
`underset(xtoa)limf(x).g(x)` exists. But if `underset(xtoa)limf(x).g(x)` exists, then
it is not necessary that both `underset(xtoa)limf(x)andunderset(xtoa)limg(x)` exists.
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