If f (x) =
`f(x)={(x^2sin, 1/x,x ne0),(0, x=0, ):}` Show that f is differentiable and continuous at x=0

Prove that f (x) =|x| is continuous at x =0

Find f {f (x)} if f(x)=(x+1)/(x-1)

If the function f(x)={{:((sin x)/(x) + cos x", if " x ne 0 ), (k", if " x =0 ):} is continuous at x=0, then find the value of k.

Show that f (x) = f(x) = {(x,sinfrac(1)(x)),(0,x=0):} is continuous at x = 0

Find the value of a for which f(x)={(sin^2(ax)/(x^2), "" xne0),(1, x=0 ""):} is continuous at x = 0

If f(x)=1/x and g(x)=0 show that fog is not defined.

If f(x)=(5x+3)/(4x-5) , (x ne 5/4) show that f{f(x)} is a identity function.

f(x)={(x^2+2x, "" xle0,),(ax+b, "" x >0,):} is continuous and differentiable at x =0, find the values of a and b

Find the value of a for which f(x)={((1-cos4x)/(8x^2), "" xne0),(a, x=0 ""):} is continuous at x = 0