The-value-of-lim-x-0-1-cos-x-2-1-cos-x-

Question Number 143960 by bobhans last updated on 20/Jun/21

The value of \lim_{x \to 0} \frac{\sqrt{1 - \cos x^{2}}}{1 - \cos x} = ?

Answered by lapache last updated on 20/Jun/21

l i \underset{x \to 0}{m} \frac{\sqrt{1 - 1 + \frac{x^{4}}{2}}}{1 - 1 + \frac{x^{2}}{2}} = l i \underset{x \to 0}{m} \frac{2 \sqrt{\frac{x^{4}}{2}}}{x^{2}} = \sqrt{2}

Answered by bramlexs22 last updated on 20/Jun/21

\lim_{x \to 0} \frac{\sqrt{2 \sin^{2} (\frac{x^{2}}{2})}}{2 \sin^{2} (\frac{x}{2})} = \frac{\sqrt{2}}{2} \lim_{x \to 0} \frac{\sin (\frac{x^{2}}{2})}{\sin^{2} (\frac{x}{2})}

= \frac{2 \sqrt{2}}{2} . 1 = \sqrt{2}