limx→0 sin2⁡x2−1+cos⁡x equals.

# $\underset{x\to 0}{lim} \frac{{\mathrm{sin}}^{2}x}{\sqrt{2}-\sqrt{1+\mathrm{cos}x}}$ equals.

1. A

$\sqrt{2}$

2. B

$2\sqrt{2}$

3. C

$4\sqrt{2}$

4. D

4

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### Solution:

So, using L' Hospital' s rule, we get

$\underset{\mid x\to 0}{lim} \frac{2\mathrm{sin}x\mathrm{cos}x}{\frac{-1}{2\sqrt{1+\mathrm{cos}x}}×\left(-\mathrm{sin}x\right)}=\underset{x\to 0}{lim} 2\mathrm{cos}x×2\sqrt{1+\mathrm{cos}x}=4\sqrt{2}$

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