#lim_(x->oo) sqrt(25x^2-9x-6)-5x+3# ?

1 Answer
Cesareo R.
Feb 27, 2018

#21/10#

Explanation:

#sqrt(25x^2-9x-6)-5x+3 = sqrt((5x-3)^2+21x-15)-(5x-3) =#

#=(sqrt((5x-3)^2+21x-15)-(5x-3))(sqrt((5x-3)^2+21x-15)+(5x-3))/(sqrt((5x-3)^2+21x-15)+(5x-3))=#

#=(21x-15)/(sqrt((5x-3)^2+21x-15)+(5x-3))=#

#(21-15/x)/(sqrt(((5x-3)/x)^2+21/x-15/x^2)+(5-3/x))# so

#lim_(x->oo)sqrt(25x^2-9x-6)-5x+3 = lim_(x->oo)(21-15/x)/(sqrt(((5x-3)/x)^2+21/x-15/x^2)+(5-3/x)) = 21/(sqrt(5^2)+5) = 21/10#

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