First slide

Introduction to limits

Question

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

Moderate

A

$- π$
B

$π$
C

$π / 2$
D

1

Solution

$lim_{x \to 0} \frac{\sin (π (\cos^{2} x)}{x^{2}} (\frac{0}{0} form)$
$\begin{array}{l} \Rightarrow lim_{a \to 0} \frac{\sin (π - π \sin^{2} x)}{x^{2}} \\ \Rightarrow lim_{α \to 0} \frac{\sin (π \sin^{2} x)}{π \sin^{2} x} \times π {(\frac{\sin x}{x})}^{2} = 1 \times π (1)^{2} = π \end{array}$

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