Category: Trigonometry

Class 10th mathmatics trigonometry important questions

Define the function

f(x)=x2sin(x21),0,x=0,x=0.

(a)

Prove that $f\left(x\right)$f(x) is continuous at $x=0$x=0.

(b)

Determine whether

$f\left(x\right)$f(x) is differentiable at $x=0$x=0. If so, find $f^{}\left(0\right)$f(0).

(c)

Find an explicit formula for $f^{}\left(x\right)$f(x) for $x0$x=0.

(d)

Decide whether

$f^{}\left(x\right)$f(x) is bounded on any neighborhood of $x=0$x=0.

(e)

Determine whether

$f^{}\left(x\right)$f(x) is Riemann integrable on $[1,1]$[1,1].