What is #lim t->-∞# of #(t^2+2)/(t^3+t^2-1)#?

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Answer 1 · 2018-05-16T08:08:50

The limit is #=0^-#

The limit is

#lim_(t->-oo)(t^2+2)/(t^3+t^2-1)#

#=lim_(t->-oo)(t^2(1+2/t^2))/(t^3(1+1/t-1/t^3)#

#=lim_(t->-oo)((1+2/t^2))/(t(1+1/t-1/t^3)#

But

#lim_(t->-oo)(2/t^2)=0#

#lim_(t->-oo)(1/t)=0^-#

#lim_(t->-oo)(1/t^3)=0^-#

Finally,

#lim_(t->-oo)(t^2+2)/(t^3+t^2-1)=lim_(t->-oo)(1/t)=0^-#