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Show that the function f(x)={x^2sin(1/x...

Show that the function `f(x)={x^2sin(1/x),ifx!=0 0,ifx=0` is differentiable at `x=0` and `f^(prime)(0)=0`

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To show that the function \[ f(x) = \begin{cases} x^2 \sin\left(\frac{1}{x}\right) & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{cases} ...
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Knowledge Check

  • The function f(x)=x^(2)"sin"(1)/(x) , xne0,f(0)=0 at x=0

    A
    is continuous but not differentiable
    B
    is discontinuous
    C
    is having discontinuous and differentiable
    D
    is continuous and differentiable

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