# DSE 2009 Doubts Classic List Threaded 5 messages Open this post in threaded view
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## DSE 2009 Doubts

 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?
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## Re: DSE 2009 Doubts

 I also had a query regarding Q.22 from part II: http://discussion-forum.2150183.n2.nabble.com/Micro-from-DSE-papers-td7577903.html
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## Re: DSE 2009 Doubts

 In reply to this post by Ayushya Kaul (5) f(x) is continuous at x=0. Check with LHL=RHL = value of the function. f(x) is clearly differentiable. Check with left hand differentiability and right hand differentiability at x=0 to see that f(x) doesn't have a "kink" at x=0. f'(x)= 2xsin(1/x)-cos(1/x) when x ≠ 0       = 0                          when x=0 now we need to check the continuity of g(x)=f'(x) the limit of g(x) is definitely ≠ 0 (infact it doesn't even exist) when x tends to zero. hence g(x) which is nothing but f'(x) is discontinuous at x=0. ---  "You don't have to believe in God, but you should believe in The Book." -Paul Erdős