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Question

Evaluate the following limits:

limx1x7-2x5+1x3-3x2+2

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Solution

When x = 1, the expression x7-2x5+1x3-3x2+2 assumes the form 00. So, (x − 1) is a factor of numerator and denominator.

Using long division method, we get

x7-2x5+1=x-1x6+x5-x4-x3-x2-x-1

and x3-3x2+2=x-1x2-2x-2

limx1x7-2x5+1x3-3x2+2=limx1x-1x6+x5-x4-x3-x2-x-1x-1x2-2x-2=limx1x6+x5-x4-x3-x2-x-1x2-2x-2=1+1-1-1-1-1-11-2-2=-3-3=1

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