MCQ
$\lim_{x \rightarrow\infty}[\sin\sqrt{x+1}-\sin\sqrt{x}]=.......$
- A2
- B4
- C7
- ✓0
=$\lim_{x \rightarrow\infty}\left[2\cos\left(\frac{\sqrt{x+1}+\sqrt{x}}{2}\right)\sin\left(\frac{\sqrt{x+1}-\sqrt{x}}{2}\right)\right]$
=$2\left[\lim_{x \rightarrow \infty}\cos\left(\frac{\sqrt{x+1}+\sqrt{x}}{2}\right)\right]\left[\lim_{x \rightarrow \infty}\sin\left\{\frac{1}{2(\sqrt{x+1}+\sqrt{x})}\right\}\right]$
=$2(\infty)(\sin0)$
=$0$
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