Solve: lim_(x→ ∞) sqrt(x)(sqrt(x)-sqrt(x-a)) ?

1 Answer
Apr 26, 2018

= a/2

Explanation:

lim_(x to oo) sqrt(x)(sqrt(x)-sqrt(x-a))

= lim_(x to oo) sqrt(x)(sqrt(x)-sqrt(x-a))* (sqrt(x)+sqrt(x-a))/(sqrt(x)+sqrt(x-a))

= lim_(x to oo) sqrt(x)* (x-(x-a))/( sqrt(x)+sqrt(x-a))

= lim_(x to oo) (a)/( 1+sqrt(1-a/x))

= (a)/( 1+ lim_(x to oo) sqrt(1-a/x)) = a/2