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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

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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