Let ,`f(x)=1/xsin(x^2)` when x `ne0`
=0 when x=0
Discuss the continuity and differentiability of f(x) at x=0.

Discuss the differentiability of f(x)=|x^3| at x=0

Let f(x)={{:((1)/(x^(2))sin(x^(2))," when "xne0),(0," when " x=0):} Discuss the continuity of f (x) at x = 0 .

Let: f(x)=int_0^x|2t-3|dtdot Then discuss continuity and differentiability of f(x)at x=3/2

A function f (x) is defined as follows : f (x)={{:(x,"when "xge0),(-x,"when " x lt0):} Examine the cotinuity and differentiability of (x) at x= 0 .

f(x)={{:(5x-4,"when "0ltxle1),(4x^(2)-3x,"when "xgt1):} Discuss the continuity and differentiability of f(x)"at" x =1

Let f(x)={(-4, -4 lexlt0),(x^2-4, 0lexle4):} Discuss the continuity and differentiability of g(x)=f(|x|)+|f(x)|

Discuss the continuity of the function f given by f(x)= |x|" at "x=0 .

A function f (x) is defined as follows : f(x)={{:(5+2x,"when " -(5)/(2)ltxle0),(5-2x,"when "0ltxlt(5)/(2)):} Examine the continuity and differentiability of f (x) at x= 0

Let {:(f(x)=5x-4," ""when "0ltxle1),(=4x^(2)-3x," ""when "xgt1):} Discuss the differentiability of f(x) at x = 1 .

If f(x)=x-2, x le 0 and 4-x^2,x > 0, then discuss the continuity of y=f(f(x)).