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Question

Evaluate the limit:
limx{x+1x}x+2

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Solution

We have,
limx{x+1x}x+2

On rationalising numerator, we get

=limx{x+1x}{x+1+x}x+2{x+1+x}

=limx{(x+1)2(x)2}x+2{x+1+x}

=limx{x+1x}x+2{x+1+x}

=limxx+2{x+1+x} ( form)

Dividing numerator and denominator by x, we get

=limxx+2x{x+1+x}x

=limx1+2x{1+1x+1}

When x, then 1x0

=1+2(0){1+(0)+1}

=1{1+1}

=12

Therefore,
limx{x+1x}x+2=12


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