First slide

Introduction to limits

Question

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

Moderate

A

0
B

1
C

-1
D

none of these

Solution

We have,
$\begin{array}{l} lim_{x \to \infty} \{\frac{x^{2} \sin (\frac{1}{x}) - x}{1 - | x |}\} \\ = lim_{x \to \infty} \frac{x^{2} \sin (x^{- 1}) - x}{1 - x} \\ = lim_{x \to \infty} \frac{(\frac{\sin (x^{- 1})}{x^{- 1}}) - 1}{x^{- 1} - 1} = \frac{1 - 1}{0 - 1} = 0 \end{array}$

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