First slide

Introduction to limits

Question

$lim_{x \to 0} \frac{\sin (π \cos^{2} x)}{x^{2}}$ equals

Moderate

A

$- π$
B

$π$
C

$\frac{π}{2}$
D

1

Solution

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

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