Can anyone help me with this limit problem?

Solve:
Lim x→ ∞ sqrt(x)(sqrt(x)-sqrt(x-a))x(xxa)

1 Answer
Mar 20, 2018

a/2a2

Explanation:

sqrt x (sqrtx-sqrt(x-a)) = x -sqrt(x(x-a))x(xxa)=xx(xa)

now

x -sqrt(x(x-a)) = (x^2-x(x-a))/(x+sqrt(x(x-a))) = (a x)/(x+sqrt(x(x-a))xx(xa)=x2x(xa)x+x(xa)=axx+x(xa)

so

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