What is the limit of # (2x^2+1)/((2-x)(2+x))# as x approaches infinity?

Question

10557 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-08T07:51:43

Limit is # -2#

#(2x^2+1)/(4-x^2)#

Divide by highest power of x:

#(2 + 1/(x^2))/(4/(x^2) - 1)#

#lim_(x->oo) (2 + 1/(x^2))/(4/(x^2) - 1) = (2+0)/(0-1) = -2#

Answer 2 · 2016-07-08T07:52:09

-2

#lim_{ x to oo} (2x^2+1)/((2-x)(2+x))#

#=lim_{ x to oo} (2+1/x^2)/((2/x-1)(2/x+1))#

#= (2)/((-1)(+1)) = -2#