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Question

Evaluate the limit:

limx15x4xx1

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Solution

Atx1,5x4xx1becomes 00form

limx15x4xx1

On rationalising numerator, we get

=limx1(5x4x)(5x4+x)(x1)(5x4+x)

=limx1((5x4)2(x)2)(x1)(5x4+x)

=limx1(5x4x)(x1)(5x4+x)

=limx1(4x4)(x1)(5x4+x)

=limx14(x1)(x1)(5x4+x)[(x1)0]

=limx14(5x4+x)

=4(5(1)4+1)

=2


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