What is the limit of #(3x^2) / (x^2+2x)# as x approaches infinity?
2 Answers
Mar 3, 2017
Explanation:
divide terms on numerator/denominator by the highest power of x, that is
#x^2#
#((3x^2)/x^2)/(x^2/x^2+(2x)/x^2)=3/(1+2/x)#
#rArrlim_(xtooo)(3x^2)/(x^2+2x)#
#=lim_(xtooo)3/(1+2/x)#
#=3/(1+0)#
#=3#
Mar 3, 2017
# lim_(x->oo) (3x^2)/(x^2+2x) =3#
Explanation:
We can manipulate the limit as follows
# lim_(x->oo) (3x^2)/(x^2+2x) = lim_(x->oo) (3x^2)/(x^2+2x) *(1/x^2)/(1/x^2)#
# " "= lim_(x->oo) (3)/(1+2/x) #
# " "= 3 #
As
