Question Number 149239 by john_santu last updated on 04/Aug/21

lim_(x→a^+ ) (((√x)−(√a) −(√(x−a)))/( (√(x^2 −a^2 )))) =?

Answered by EDWIN88 last updated on 04/Aug/21

lim_(x→a^+ ) ((((√(x−a)))^2 )/(((√x)+(√a))(√((x−a)(x+a)))))−lim_(x→a^+ ) ((√(x−a))/( (√(x−a)) (√(x+a)))) = lim_(x→a^+ ) ((√(x−a))/(((√x)+(√a))(√(x+a))))−lim_(x→a^+ ) (1/( (√(x+a)))) = 0−(1/( (√(2a))))=−(1/( (√(2a))))