Can anyone help me with this limit problem?

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

1 Answer
Mar 20, 2018

Answer:

#a/2#

Explanation:

#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#