Can anyone help me with this limit problem?

Question

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

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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#