Lim x- ∞ x+x^2/1-2x^2 ?

Question

lim x- ∞ x+x^2/1-2x^2

5681 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-21T23:05:50

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

If we plug in infinity into the limit, we have an #oo/(-oo)# situation.

We have to use #color(red)("L'Hôpital's rule")#, by taking the derivative of both the numerator and denominator.

#lim_(x->oo) (x+x^2)/(1-2x^2) = lim_(x->oo) (d/dx(x+x^2))/(d/dx(1-2x^2))#

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

Since #x# grows boundless, #-1/(4x)# approaches #0#.

#color(red)( :. lim_(x->oo) (x+x^2)/(1-2x^2)=-1/2#