lim-x-pi-pi-pi-4x-cos-pi-x-1-2-

Question Number 84364 by jagoll last updated on 12/Mar/20

\lim_{x \to π} \frac{\sqrt{π} - \sqrt{π + 4 x}}{\cos (\frac{π (x + 1)}{2})} = ?

Answered by john santu last updated on 12/Mar/20

\sqrt{π} \times \lim_{x \to π} \frac{1 - \sqrt{1 + \frac{4 x}{π}}}{- \sin (\frac{π x}{2})} =

- \sqrt{π} \times \lim_{x \to π} \frac{1 - (1 + \frac{2 x}{π} + o (x))}{\frac{π x}{2}} =

- \sqrt{π} \times \frac{2}{π} \times - \frac{2}{π} = \frac{4 \sqrt{π}}{π^{2}}