Let `f(x) = {:{(1-x^2,xle0),(1+x^2,x>0):}`.
Find Lf' (0)Rf'(0). Is f derivable at x = 0?

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

Let f(x) = {:{((1-cos2x)/(2x^2), x 0):} . Find k if f is continous at 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) = {:{(|x| for 0<|x|le1), (1 for x = 0):} then

Let f(x) = {:{((1-cosax)/(xsinx), x ne 0),(1/2, if x = 0):} If f is continuous at x=0, find a.

Let f(x) = (2^(1/x))/(1+2^(1/x)) for x ne 0 . Find f(0) if f is right continuous at x = 0

Let f(x) = x^3/3-x^2/2+x-16 . Find f’(0), f’(-1).

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

Let f(x) = (e^(1//x))/(1+e^(1//x)) for x ne 0 . Find f (0) if f is left continuous at x = 0

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1