`Let f(x) ={{:((cos""(1)/(x))(log(1+x))^(2),xge0),(0,xle0):}`. Prove that f(x) if differentiable but derivative is not continuous at x=0.

If f(x)= {{:(,(x log cos x)/(log(1+x^(2))),x ne 0),(,0,x=0):} then

Let f(x)={{:((log(1+ax)-log(1-bx))/x, x ne 0), (k,x=0):} . Find 'k' so that f(x) is continuous 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

Let f(x)={{:(,x^(n)sin\ (1)/(x),x ne 0),(,0,x=0):} Then f(x) is continuous but not differentiable at x=0 . If

If f(x)={xe^-[1/(|x|)+1/x]; x != 0; 0;x=0 Prove that f(x) is not differentiable at x = 0

If f(x)={(1-cosx)/(xsinx),x!=0 and 1/2,x=0 then at x=0,f(x) is (a)continuous and differentiable (b)differentiable but not continuous (c)continuous but not differentiable (d)neither continuous nor differentiable

If f(x)={(1-cosx)/(xsinx),x!=0 and 1/2,x=0 then at x=0,f(x) is (a)continuous and differentiable (b)differentiable but not continuous (c)continuous but not differentiable (d)neither continuous nor differentiable

Let f(x) = {:{ (x sin""(1/x) , x ne 0) , ( k , x = 0):} then f(x) is continuous at x = 0 if

Prove that f(x) = {sinx/x ; x != 0 and 1 ; x=0 . is continuous at x=0 .

Let f(x) = {{:((cos x-e^(x^(2)//2))/(x^(3))",",x ne 0),(0",",x = 0):} , then Statement I f(x) is continuous at x = 0. Statement II lim_(x to 0 )(cos x-e^(x^(2)//2))/(x^(3)) = - (1)/(12)