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

Show that the function f(x) = {:{(x^n sin(1/x), x ne 0),(0, x = 0):} is continuous but not differentiable at x= 0.

Show that the function defined by f(x) = {{:(x^(2) sin 1//x",",x ne 0),(0",",x = 0):} is differentiable for every value of x, but the derivative is not continuous for x=0

Show that the function: f(x) = {:{(2+x,ifxge0),(2-x,ifx<0):} is continuous but not derivable at x=0

Let f(x)={(xsin(1/x), x ne 0),(k, x=0):} find k if f is continuous at x=0,

Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is a. differentiable both at x = 0 and at x = 2 b. differentiable at x = 0 but not differentiable at x = 2 c. not differentiable at x = 0 but differentiable at x = 2 d. differentiable neither at x = 0 nor at x = 2

Show that f(x)={{:("x sin"(1)/(x)",","when",x ne 0),(0",","when",x = 0):} is continuous but not differentiable at x = 0

Let f(x) = {:{((sinx)/x + cosx, when x ne 0),(2, when x = 0):} show that f (x) is continouous at x = 0.

A function f : R rarr R satisfies the equation f(x + y) = f(x) . f(y) for all, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

Examine the derivability of: f(x) = {:{(x^2sin(1/x),xne0),(0,x=0):} at x =0

Let f: R to R satisfies |f(x)|lex^(2)AAx in R. then show thata f(x) is differentiable at x=0