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Question

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


A

True

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B

False

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Solution

The correct option is A

True


If both the limits limxaf(x) and limxag(x) exist finitely, then we can apply the limits independently to them in a limit involving both of them and xa, provided the limit does not become indeterminate or infinite.
This is also true for taking exponents, like f(x)g(x).


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