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Question

Evaluate the limit:

limx21+4x5+2xx2

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Solution

At x2,

1+4x5+2xx2 becomes00form

limx21+4x5+2xx2

On rationalising numerator, we get

=limx2(1+4x5+2x)(1+4x+5+2x)(x2)(1+4x+5+2x)

=limx2((1+4x)2(5+2x)2)(x2)(1+4x+5+2x)

[(ab)(a+b)=a2b2]

=limx2(1+4x52x)(x2)(1+4x+5+2x)

=limx2(2x4)(x2)(1+4x+5+2x)

=limx22(x2)(x2)(1+4x+5+2x)[(x2)0]

=limx22(1+4x+5+2x)

=2(1+4(2)+5+2(2))

2(9+9)

=23+3

=26

=13

Therefore,

limx21+4x5+2xx2=13


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