Let fx- left begin matrix x-1 sinsinac1x-1- - if - x n e q 10- - if x-1Iend matrix right- Then- which one of the following is true-

The correct option is C f is differentiable at x = 0 but not at x = 1 L.H.D: x→ 1^ lim[(x 1)sin1/(x 1) 0/x 1 ] R.H.D: x→ 1^+lim[(x 1)sin1/(x 1) 0/x 1 ] L.H.D ...

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Byju's Answer

Standard XII

Mathematics

Right Hand Derivative

Let fx=⟨ left...

Question

Let $f (x) = {\begin{matrix} (x - 1) s i n \frac{1}{x - 1}, & i f x \neq 1 0, & i f x = 1 \end{matrix}$ Then, which one of the following is true?

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

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

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f is differentiable at x = 0 and x = 1

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

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Solution

The correct option is D f is differentiable at x = 0 but not at x = 1
$L . H . D : - l i m x \to 1^{-} [\frac{(x - 1) s i n \frac{1}{(x - 1)} - 0}{x - 1}] R . H . D : - l i m x \to 1^{+} [\frac{(x - 1) s i n \frac{1}{(x - 1)} - 0}{x - 1}] L . H . D \neq R . H . D$

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Let f(x)={(x−1)sin1x−1,if x≠10,ifx=1 Then, which one of the following is true?

The correct option is D f is differentiable at x = 0 but not at x = 1 L.H.D:−limx→1−[(x−1)sin1(x−1)−0x−1]R.H.D:−limx→1+[(x−1)sin1(x−1)−0x−1]L.H.D≠R.H.D

Let $f (x) = {\begin{matrix} (x - 1) s i n \frac{1}{x - 1}, & i f x \neq 1 0, & i f x = 1 \end{matrix}$ Then, which one of the following is true?

The correct option is D f is differentiable at x = 0 but not at x = 1
$L . H . D : - l i m x \to 1^{-} [\frac{(x - 1) s i n \frac{1}{(x - 1)} - 0}{x - 1}] R . H . D : - l i m x \to 1^{+} [\frac{(x - 1) s i n \frac{1}{(x - 1)} - 0}{x - 1}] L . H . D \neq R . H . D$