Can anyone help me with this limit problem?

Question

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

1191 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-20T15:37:21

$a/2$

$sqrt x (sqrtx-sqrt(x-a)) = x -sqrt(x(x-a))$

now

$x -sqrt(x(x-a)) = (x^2-x(x-a))/(x+sqrt(x(x-a))) = (a x)/(x+sqrt(x(x-a))$

so

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