The value of limx→1^(-)⁡(√(2π)-√(4sin^(-1)⁡x))/(√(1-x)) is equal to

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MARKS Content Team · Accepted Answer

Correct answer: (D) 2/(√(π)). We have, limx→1^(-)⁡(√(π)-√(2sin^(-1)⁡x))/(√(1-x))√2 =limx→1^(-)⁡(√(π)-√(2sin^(-1)⁡x))/(√(1-x))×(√(π)+√(2sin^(-1)⁡x))/(√(π)+√(2sin^(-1)⁡x))×√2 =limx→1^(-)⁡(2√2π)/2-sin^(-1)⁡x√(1-x)√(π)+√(2sin^(-1)⁡x) =limx→1^(-)⁡(2√2cos^(-1)⁡x)/(√(1-x))⋅1/(2√(π)) =limθ→0^(+)⁡(2√2θ)/(√2sin⁡θ2)⋅1/(2√(π)) [Putting x=cos⁡θ ] =(4√2)/(2√(2π))=2/(√(π))

The value of $\lim_{x \to 1^{-}} \frac{\sqrt{2 π} - \sqrt{4 \sin^{- 1} x}}{\sqrt{1 - x}}$ is equal to

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More Limits Questions

The value of limx→1-⁡2π-4sin-1⁡x1-x is equal to

Solution

More Limits Questions

The value of $\lim_{x \to 1^{-}} \frac{\sqrt{2 π} - \sqrt{4 \sin^{- 1} x}}{\sqrt{1 - x}}$ is equal to