Let f(x) = x+|x|. Show that f is not derivable at x = 0.

Let f(x) = x+ |x|. Show that f is continuous but not derivable at x = 0

Show that the function f(x) = {{:(-x^2, x le 0),(x^2 ,x gt 0):} is continuous at x = 0 . Also show that f is differentiable at x = 0 .

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

Let f: Rrarr R and g: RrarrR be defined by f(x) = x^2 and g(x) = x + 1 . show that gof is not equal to fog .

Let f (x) = |x|, then f(-5/2) is :

Let f= R rarr R be defined by f(x)=3x-7. Show that f is invertible.

Let f(x) = (x - a) cos (1/(x-a)) for x ne a and le f (a) = 0. Show that f is continuous at x = a but not derivable thereat.

Let f (x) = x |x|, then f (0) is equal to

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