Let f(x)={\\begin{array}{c}(x-1) \sin \\\\\\{1\end\frac{array}{x-1} , \text{ if } x \neq 1 ; 0 , \text{ if } x=1}. Then which one of the following is true? [AIEEE 2008]

Correct Answer is : f is differentiable at x=0 but not at x=1

f is neither differentiable at x=0 nor at x=1

f is differentiable at x=0 and at x=1

f is differentiable at {\x}=0 but not at {\x}=1

f is differentiable at x=1 but not at x=0

AIEEE 2008 Solved Paper

Section: Mathematics

Question : 102 of 104

Marks: +1, -0

Let f(x)={

(x−1)‌sin‌‌

x−1

‌ if ‌x≠1

‌ if ‌x=1

.
Then which one of the following is true?

[AIEEE 2008]

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