If `f` is an even function such that `(lim)_(hvec0)(f(h)-f(0))/h` has some finite non-zero value, then prove that `f(x)` is not differentiable at `x=0.`

If f is an even function, prove that lim_(xto0^(-)) (x)=lim_(xto0^(+)) f(x).

Which of the function is non-differential at x=0?f(x)=x|x|

If an even function f is differentiable at x=0, then f '(0)=

If f(x) is a differentiable function of x then lim_(h rarr0)(f(x+3h)-f(x-2h))/(h)=

If f is an even function,then prove that lim_(x rarr0^(-))f(x)=lim_(x rarr0^(+))f(x)

If f is derivable function of x, then underset(hto0)("lim")(f(x+h)-f(x-h))/(h)=

the value of lim_(h to 0) (f(x+h)+f(x-h))/h is equal to

Let f(x) be a real valued function such that f(a)=0. If g(x)=(x-a)f(x) is continuous but notdifferentiable at x=a and h(x)=(x-a)^(2)f(x) is continuous and differentiable at x=a .Then f(x)

Which of the function is non-differential at x=0?f(x)=cos|x|

Which of the function is non-differential at x=0?f(x)=|x^(3)|