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

if f(x)={(x^2,xle1),(ax+b,x>1):} is differentiable at x = 1, find the values of a and b. Hence find f'(1)

If 2x = 0, find x.

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.

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

If -1/2 is a root of the quadratic equation 2x^2+ax-3=0 ,find the value of a.

Examine differentiability at x= 1 and x=0 f(x)={(-x, x 1, ):}