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

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

Grade:12th pass

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 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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