Q: Let {(x^{m}\sin\frac{1}{x};,x \ne 0),(0;,x=0):} Find the set of values of

David Young

David Young

Answered question


Q: Let {xmsin1x;x00;x=0
Find the set of values of m for which
(i) f(x) is continuous at x=0
(ii) f(x) is differentiable at x=0
(iii) f(x) is continuous but not differentiable at x=0.

Answer & Explanation

Bernard Lacey

Bernard Lacey

Beginner2021-12-27Added 30 answers

The given function is:
i) f is continuous at x=0 if
Now, limx0f(x)
x=0 is m>0
limx0f(0)0 if m<0
δ0 f is continuous for mt(0,)
Jenny Bolton

Jenny Bolton

Beginner2021-12-28Added 32 answers

ii) Now, f(x)=mxm1sin1x+xmcos(1x)(1x2)
mxm1sin(1x)xm2cos(1x) if x0
So, it is differentiable at x=0
if m>2 because then only 
f(x) is differentiable 
Hence, f is continuous but only differentiable at x=0 if m[2,)



Expert2022-01-09Added 613 answers

iii) So, f is continuous but only differentiable at
is on (0, 2)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?