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Question

Evaluate the mentioned limit:
limx1x72x5+1x33x2+2

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Solution

Given: limx1x72x5+1x33x2+2 becomes 00 form

Using Factorization method

Now, numerator

x72x5+1

=(x1)(x6+x5x4x3x2x1)

Also, denominator

x33x2+2=(x1)(x22x2)

limx1x72x5+1x33x2+2

=limx1(x1)(x6+x5x4x3x2x1)(x1)(x22x2)

=limx1(x6+x5x4x3x2x1)(x22x2)

=(16+1514131211)(122(1)2)

=33=1

limx1x72x5+1x33x2+2=1


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