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Question Number 86655 by jagoll last updated on 30/Mar/20

lim_(x→−1^+ )  (((√π) −(√(arc cos x)))/(√(x+1)))

limx1+πarccosxx+1

Answered by john santu last updated on 30/Mar/20

L′hopital rule  lim_(x→−1^+ )  ((−(1/2)(arc cos x)^(−(1/2)) (((−1)/(√(1−x^2 )))))/(1/(2(√(x+1)))))   lim_(x→−1^+ )  (1/(√(arc cos x))) ×((√(1+x))/(√(1−x^2 )))  lim_(x→−1^+ )  (1/(√(arc cos x)))×(1/(√(1−x)))  (1/(√π)) × (1/(√2))  = (1/(√(2π)))

Lhopitalrulelimx1+12(arccosx)12(11x2)12x+1limx1+1arccosx×1+x1x2limx1+1arccosx×11x1π×12=12π

Commented by jagoll last updated on 30/Mar/20

thank you

thankyou

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