Flag Integral Calculus> 1.lim (pi) 0.5 – (cos -1 x) 0.5 /(x + 1) ...
question mark

1.lim (pi)0.5 – (cos-1x)0.5 /(x + 1)0.5
x--->-1+

Arpit Dhankar , 10 Years ago
Grade 12th pass
anser 1 Answers
Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

L = \lim_{x\rightarrow -1^{+}}(\frac{\sqrt{\pi }-\sqrt{cos^{-1}x}}{\sqrt{x+1}})
This is zero by zero form, use L’hospital rule

L = \lim_{x\rightarrow -1^{+}}(\frac{-2\sqrt{1+x}}{2\sqrt{cos^{-1}x}}.\frac{-1}{\sqrt{1-x^2}})
L = \lim_{x\rightarrow -1^{+}}(\frac{1}{\sqrt{cos^{-1}x}}.\frac{1}{\sqrt{1-x}})
L = (\frac{1}{\sqrt{\pi }}.\frac{1}{\sqrt{1+1}})
L = \frac{1}{\sqrt{2\pi }}

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