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

1 Answer
Ultrilliam
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#

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