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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
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 Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Askiitians Experts Badiuddin
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 Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Askiitians Experts Badiuddin
=lim x tends to 0- xn-1 sin1/x
LHD =RHD only possible for n>=1
Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Askiitians Experts Badiuddin
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