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for the function to be cont & diff at x=0. what will be the value of n? f(x) = x n sin 1/x x not 0 0 x =0

for the function to be cont & diff at x=0.


what will be the value of n?


f(x) =      xn sin 1/x        x not 0


                  0                 x =0

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear dinesh

f(x) =      xn sin 1/x        x not 0

                  0                 x =0

for differentiability at x=0

RHD     f'(0)= lim x tends to 0+  {f(x)-f(0)}/(x-0)

                    =lim x tends to 0+  xn-1 sin1/x

                    limit exixt for n>=1    and sin(1/x)   always lies between -1 to 1

                  

LHD f'(0)= lim x tends to 0-     {f(x)-f(0)}/(x-0)

                    =lim x tends to 0-        xn-1 sin1/x

                    limit exixt for n>=1    and sin(1/x)   always lies between -1 to 1

   LHD =RHD  only possible for n>=1


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