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 is an even function such that lim_(h rarr 0) (f(h)-f(0))/(h) has some fininte non-zero value, then

If f is an even function, then prove that lim_(x->0^-) f(x) = lim_(x->0^+) f(x)

If f(x) is a twice differentiable function such that f(0)=f(1)=f(2)=0 . Then

If [.] is the greatest integer function and f(x)=[tan^2x], then (a) ("lim")_(xvec0)f(x) does not exist (b) f(x) is continuous at x=0 (c) f(x) is not differentiable at x=0 (d) f^(prime)(0)=1

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

If f is an even function , then prove that Lim_( xto 0^(-)) f(x) = Lim_(x to 0^(+)) f(x) , whenever they exist .

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

If f is real-valued differentiable function such that f(x)f'(x)<0 for all real x, then

If f is real-valued differentiable function such that f(x)f'(x)<0 for all real x, then

Let f(x) be a function defined on (-a ,a) with a > 0. Assume that f(x) is continuous at x=0a n d(lim)_(xvec0)(f(x)-f(k x))/x=alpha,w h e r ek in (0,1) then f^(prime)(0^+)=0 b. f^(prime)(0^-)=alpha/(1-k) c. f(x) is differentiable at x=0 d. f(x) is non-differentiable at x=0