If `f(x)= xsin(1/x), x!=0` and `f(x)=0, x=0` then show that `f'(0)` does not exist

Let f be defined on R by f(x)= x^(4)sin(1/x) , if x!=0 and f(0)=0 then (a) f'(0) doesn't exist (b) f'(2-) doesn't exist (c) f'' is not continous at x=0 (d) f''(0) exist but f'' is not continuous at x=0

Let f be defined on R by f(x)=x^(4)sin(1/x) , if x!=0 and f(0)=0 then (a) f'(0) doesn't exist (b) f'(2-) doesn't exist (c) f'' is not continous at x=0 (d) f''(0) exist but f''' is not continuous at x=0

If f(x) = (|x|)/x then show that Lt_(x to 0) f(x) does not exist.

If f(x)=(|x|)/(x) , then show that lim_(xrarr0) f(x) does not exist.

If f(x)=(|x|)/(x) , then show that lim_(xrarr0) f(x) does not exist.

If f(x)={:{(1+sin x", " 0 le x lt pi//2),(" "1 ", " x lt0):} then show that f'(0) does not exist.

If f(x)={(x-|x|)/x ,x!=0, 2,x=0 , show that lim_(xrarr0) f(x) does not exist.

If f(x) = {:{(xsin(1/x),xne0),(0,x=0):} Show that 'f' is not differentiable at x =0

Given f(x)={((x+|x|)/x,x!=0),(-2,x=0):} show that lim_(xto0)f(x) does not exist.

If f(x) = (|x|)/(x) (x != 0) , then show that underset(x rarr 0)lim f(x) does not exists.