Question

lim ₓ→₁₋ [√π – √(2sin⁻¹ x)]/√(1 – x)
is equal to :
(A) 1/√(2π)
(B) √(2/π)
(C) √(π/2)
(D) √(π)

Answer 1

Question ;

lim ₓ→₁₋ [√π – √(2sin⁻¹ x)]/√(1 – x)

$\huge{ \underline{ \underline{ \green{ \sf{ Detailed \: Answer :}}}}}$

It is an 0/0 form

so for solving the question , we use L- Hospital rule .

For step by step explanation refer to the attachment.

${\purple{\boxed{\large{\bold{</p><p> \lim_{ \Delta x \to \: 1{}^{-1}}\frac{ \sqrt{\pi} - \sqrt{2 \sin {}^{ - 1} (x) } }{ \sqrt{1 - x} }\\</p><p>=\sqrt{ \frac{2}{\pi} }}}}}}$

correct option b)