Q104 / 160 · AP EAMCET 2022 (06 Jul Shift 2) · Mathematics

[.] represents the greatest integer function. At $x=-1, \frac{d}{d x} \sin \pi[x]=$

  • Correct answer
    A
    0
  • B
    2
  • C
    -2
  • D
    $1 / 2$

Solution

$\begin{aligned} & \text { Let } y=[x] \\ & y \in z \\ & \Rightarrow \quad \sin \pi y=0 \\ & \Rightarrow \quad \frac{d}{d x} \sin \pi[x]=0 \Rightarrow \frac{d}{d x} \sin \pi[-1]=0\end{aligned}$

Hence, the correct answer is option: 'A'.

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