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Let \mathrm{a} \in \mathbb{Z} and [t] be the greatest integer \leq \mathrm{t}.Then the number of points, where the function \mathrm{f}(\mathrm{x})=[\mathrm{a}+13 \sin$ $\mathrm{x}], \mathrm{x} \in(0, \pi)is not differentiable, is_____.

Option: 1

25


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

f(x)=[a+13 \sin x]=a+[13 \sin x] \text { in }(0, \pi)
\mathrm{x} \in(0, \pi)
\Rightarrow 0<13 \sin \mathrm{x} \leq 13
\Rightarrow[13 \sin x]=\{0,1,2,3, \ldots 12,13,\}
                                       \downarrow                   \downarrow     \downarrow
                                       2                    2     1

Total point of N.D. = 25.

Posted by

himanshu.meshram

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