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Question

If limxaf(x)=L and limxag(x)=m, then limxa(f(x))g(x)=Lm


A

True

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B

False

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Solution

The correct option is B

False


If both the limits limxaf(x) and limxag(x) exists finitely, then we can apply the limits independently to them in a limt involving both of them and xa, provided the limit does not become indeterminate or infinite.
This is true for taking powers also, like f(x)g(x). We do not need the exact proof of this. A fair intuition is good enough to understand coming concepts and solve problems.


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