Let a and [ t ] be the greatest integer t . Then the number of points, where the function f ( x ) = [ a + 13 sin x ] , x ( 0 ) is not differentiable, is _______. [2023]

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Solution

Q.
Let $a \in ℤ$ and $[t]$ be the greatest integer $\leq t$ . Then the number of points, where the function $f (x) = [a + 13 \sin x], x \in (0, π)$ is not differentiable, is _______. [2023]

Ans.
(25)

Let $f (x) = [a + 13 \sin x]$

$∵$ $a \in ℤ$ and $x \in (0, π)$ and $p$ is prime.

Total number of points of non-differentiability of $[a + p \sin x] = 2 p - 1$

Here $p = 13$

Thus, total number of non-differentiability points are $2 \times 13 - 1 = 25 .$

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