DSE 2009 Doubts

Posted by Ayushya Kaul on Jun 23, 2013; 8:16pm
URL: http://discussion-forum.276.s1.nabble.com/DSE-2009-Doubts-tp7582814.html

Could anyone take a look at question 5 from PART-II of DSE 2009?

5. Consider the function
f(x)= x^2. sin(1/x) if x=/ 0
     =0                  if x=0
Then the following is true about the derivative of f :
a) 1 f )0(' = − and ) f (' x is continuous at x = 0.
b) f )0(' = −1 and ) f (' x is discontinuous at x = 0.
c) f )0(' = 0 and ) f (' x is discontinuous at x = 0.
d) f (' x)is not defined at x = 0.


Basically, I don't know how to solve the LHL and RHL. Could anyone show the steps for it?