limx→1 x8−2x+1×4−2x+1 equals

$\underset{x\to 1}{lim} \frac{{x}^{8}-2x+1}{{x}^{4}-2x+1}$ equals

1. A

3

2. B

0

3. C

-3

4. D

1

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Solution:

We have,

$\begin{array}{l}\underset{x\to 1}{lim} \frac{{x}^{8}-2x+1}{{x}^{4}-2x+1}\\ =\underset{x\to 1}{lim} \frac{\left(x-1\right)\left({x}^{7}+{x}^{6}+{x}^{5}+{x}^{4}+{x}^{3}+{x}^{2}+x-1\right)}{\left(x-1\right)\left({x}^{3}+{x}^{2}+x-1\right)}\\ =\underset{x\to 1}{lim} \frac{{x}^{7}+{x}^{6}+{x}^{5}+{x}^{4}+{x}^{3}+{x}^{2}+x-1}{{x}^{3}+{x}^{2}+x-1}=\frac{6}{2}=3\end{array}$

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