First slide

Introduction to limits

Question

The value of $lim_{x \to \infty} {(\frac{x^{2} - 2 x + 1}{x^{2} - 4 x + 2})}^{x}$ , is

Moderate

A

$e^{2}$
B

$e^{2 - 1}$
C

$e^{6}$
D

none of these

Solution

We have,
$\begin{array}{l} lim_{x \to \infty} {(\frac{x^{2} - 2 x + 1}{x^{2} - 4 x + 2})}^{x} \\ = lim_{x \to \infty} {(1 + \frac{2 x - 1}{x^{2} - 4 x + 2})}^{x} = e^{x \to \infty} \frac{(2 x - 1) x}{x^{2} - 4 x + 2} = e^{2} \end{array}$

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