lim-x-1-pi-arc-cos-x-x-1-

Question Number 86655 by jagoll last updated on 30/Mar/20

\lim_{x \to - 1^{+}} \frac{\sqrt{π} - \sqrt{arc \cos x}}{\sqrt{x + 1}}

Answered by john santu last updated on 30/Mar/20

L^{'} hopital rule

\lim_{x \to - 1^{+}} \frac{- \frac{1}{2} {(arc \cos x)}^{- \frac{1}{2}} (\frac{- 1}{\sqrt{1 - x^{2}}})}{\frac{1}{2 \sqrt{x + 1}}}

\lim_{x \to - 1^{+}} \frac{1}{\sqrt{arc \cos x}} \times \frac{\sqrt{1 + x}}{\sqrt{1 - x^{2}}}

\lim_{x \to - 1^{+}} \frac{1}{\sqrt{arc \cos x}} \times \frac{1}{\sqrt{1 - x}}

\frac{1}{\sqrt{π}} \times \frac{1}{\sqrt{2}} = \frac{1}{\sqrt{2 π}}

Commented by jagoll last updated on 30/Mar/20

thank you

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