lim-x-0-1-xsin-x-cos-2x-tg-2-x-2-

Question Number 26363 by d.monhbayr@gmail.com last updated on 24/Dec/17

\lim_{x \to 0} \frac{\sqrt{1 + x \sin x} - \sqrt{\cos 2 x}}{{t g}^{2} \frac{x}{2}}

Commented by kaivan.ahmadi last updated on 24/Dec/17

= li \underset{x \to 0}{m} \frac{\sqrt{1 + x^{2}} - \sqrt{1 - {2 x}^{2}}}{\frac{x^{2}}{4}} \overset{hop}{=}

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

li \underset{x \to 0}{m} \frac{2}{\sqrt{1 + x^{2}}} + \frac{4}{\sqrt{1 - {2 x}^{2}}} = 2 + 4 = 6