Let fx=(x-1)sin1x-1 if x≠10 if x=1 Then which one of the following is true?
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a
f is differentiable at x=0 and x=1
b
f is differentiable at x=0 but not at x=1
c
f is differentiable at x=1 but not at x=1
d
f is neither differentiable at x=0 nor at x=1
answer is B.
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Detailed Solution
The given function is fx=x−1sin1x−1 if x≠10 if x=1At x=0 the function is differentiableAt x=1Rf'1=limh→0f1+h−f1h=limh→0hsin1hh=limh→0sin1h does not exist