Question

Evaluate
$\rm \displaystyle \lim_{n\to 1}\ \frac{x^{4}-3x^{2}+2}{x^{3}-5x^{2}+3x+1}$

Answer 1

Solution :

$\rm \displaystyle \lim_{x\to 1}\ \frac{x^{4}-3x^{2}+2}{x^{3}-5x^{2}+3x+1}$
= $\rm \displaystyle \lim_{x\to 1}\ \frac{[(x-1)(x^{3}+x^{2}-2x-2)]}{[(x-1)(x^{2}-4x-1)]}[\tex]\\ = [tex]\rm \displaystyle \lim_{x \to 1}\ \frac{(x^{3}+x^{2}-2x-2)}{(x^{2}-4x-1)}$

= ( 1 + 1 - 2 - 2 )/( 1- 4 - 1 )

= (-2)/(-4)

= 1/2

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