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

                  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+  x^n-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-        x^n-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