Question

Among the following equations the one that most accurately describes the graph shown below is

• A. $y=x\sin \frac{\pi }{x};0<x<1$
• B. $y=x\cos \frac{\pi }{x};0<x<1$
• C. $y=\frac{1}{x}\sin \left(\pi x\right);0<x<1$
• D. $y=\frac{1}{x}\cos \left(\pi x\right);0<x<1$

Answer 1

Answer: (B)

$y=x\cos \frac{\pi }{x};0<x<1$

At $x=0$,

$f\left(x\right)⟶0$

Also the function is increasingly periodic,

$\therefore$ the function is either $xsin\left(\frac{\pi }{x}\right)$ or $xcos\left(\frac{\pi }{x}\right)$

But $f\left(x\right)⟶0$ as $x⟶0$

$\therefore$The function is $x\cos \left(\frac{\pi }{x}\right)$