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Evauate lim(xto1) (x^(4)-3x^(4)+2)/(x^(3...

Evauate `lim_(xto1) (x^(4)-3x^(4)+2)/(x^(3)-5x^(2)+3x+1).`

Text Solution

Verified by Experts

The correct Answer is:
`5//4`
We have `L=underset(xto1)lim(x^(4)-3x^(3)+2)/(x^(3)-5x^(2)+3x+1)`
Clearly x=1 is zero of Nr. And Dr.. So, factorizing, we get
`L=underset(xto1)lim((x-1)(x^(3)-2x^(2)-2x-2))/((x-1)(x^(2)-4x-1))`
`=underset(xto1)lim(x^(3)-2x^(2)-2x-2)/(x^(2)-4x-1)=(1-2-2-2)/(1-4-1)=5/4`
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