2. The function f(x)=x^2/|x| when x not = 0, & 0 when x=0. Then(a) is not continuous at x = 0(b) continuous at x = 0, but not differentiable(c) differentiable once, but not twice(d) differentiable infinitely many times

Dear Arnab Das      ,
 
 f(x)=x^2/|x|

 f(x)= x   when x>o
 
     = -x  when x<0
     
     = 0   when x=0
 

 so the function is continous for all x
 
 and the function is not differentiabele at x =0
 
 so the answer b is the right one
 
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