First slide

Introduction to limits

Question

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

Moderate

A

3
B

0
C

-3
D

1

Solution

We have,
$\begin{array}{l} lim_{x \to 1} \frac{x^{8} - 2 x + 1}{x^{4} - 2 x + 1} \\ = lim_{x \to 1} \frac{(x - 1) (x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x - 1)}{(x - 1) (x^{3} + x^{2} + x - 1)} \\ = lim_{x \to 1} \frac{x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x - 1}{x^{3} + x^{2} + x - 1} = \frac{6}{2} = 3 \end{array}$

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