Question:
At how many points between the interval $ \left(-\infty, \infty\right)$ is the function $f (x) = sin\, x$ is not differentiable.
At how many points between the interval $ \left(-\infty, \infty\right)$ is the function $f (x) = sin\, x$ is not differentiable.
Updated On: Apr 26, 2024
- $0$
- $7$
- $9$
- $3$
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The Correct Option is A
Solution and Explanation
The function $f (x) = sin \,x $is differentiable for all $x\,\in\,R.$ Therefore the number of pointsin the interval $\left(-\infty, \infty\right)$ where the function is not differentiable are zero.
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Concepts Used:
Continuity & Differentiability
Definition of Differentiability
f(x) is said to be differentiable at the point x = a, if the derivative f ‘(a) be at every point in its domain. It is given by
Definition of Continuity
Mathematically, a function is said to be continuous at a point x = a, if
It is implicit that if the left-hand limit (L.H.L), right-hand limit (R.H.L), and the value of the function at x=a exist and these parameters are equal to each other, then the function f is said to be continuous at x=a.
If the function is unspecified or does not exist, then we say that the function is discontinuous.