Question

A curve is represented by y=sin x. If x is changed from $\frac{\pi }{3}to\frac{\pi }{3}+\frac{\pi }{100}$, find approximately the change in y.

• A. $\frac{\pi }{100}$
• B. $\frac{\pi }{200}$
• C. $\frac{1}{2}$
• D. None of these

Answer 1

The correct option is B

$\frac{\pi }{200}$

y= sinx
$\frac{dy}{dx}$ is instantaneous rate of change = cosx
Question is asking change in y i.e. $△$y
given $△$x i.e., $\frac{\pi }{3}to\frac{\pi }{3}+\frac{\pi }{100}$
$\Rightarrow △x=\frac{\pi }{100}$
Since rate is asked to be assumed approximately the same as instantaneous rate so
$\frac{dy}{dx}=\frac{△y}{△x}$
$\frac{dy}{dx}atx=\frac{\pi }{3}=cos\frac{\pi }{3}=\frac{1}{2}$
$\frac{1}{2}=\frac{△y}{\frac{\pi }{100}},△y=\frac{\pi }{200}$