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Question

Let f:R[0,) be such that limx5f(x) exists and limx5(f(x))29|x5|=0. Then limx5f(x) equal

A
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Solution

The correct option is A 3
Given: f:R[0,):limx5f(x)

Given: limx5(f(x))29|x5|=0
limx5(f(x))29|x5|=0

We know that denominator cannot be zero|x5|0
So for making limx5(f(x))29|x5| equal to zero,
limx5[f(x)]29 should be equal to zero.

limx5(f(x))29=0
limx5(f(x))2=9
limx5f(x)=±3

limx5f(x)3[f:R(0,)]
limx5f(x)=3

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