How do you evaluate the limit #(1-4x^3)/(x^2+2x+1)# as x approaches #oo#?

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Answer 1 · 2018-07-12T11:18:29

#pm infty#

writing

#(x^3(1/x^3-4))/(x^2(1+2/x+1/x^2))#
and this is

#x*(1/x^3-4)/(1+2/x+1/x^2)#

Answer 2 · 2018-07-12T11:27:50

#-oo#

#lim_(x to oo) (1-4x^3)/(x^2+2x+1)#

#=lim_(x to oo) (1-4x^3)/((x+1)^2 )#

For #x">>"1 qquad {(1 - 4x^3 to -4x^3),((x+1)^2 to x^2):}#

#=lim_(x to oo) ( -4x^3)/(x^2 )#

#= -4 lim_(x to oo) x = - oo#