How do you find the limit of # [ ( t^2 + 2) / (t^3 + t^2 -1) ]# as t approaches #oo#?

1 Answer
Truong-Son N.
Aug 5, 2016

As #t->oo#, #t^2# in the numerator and #t^3# in the denominator increase fastest amongst the other terms, so #2# becomes insignificant, #-1# becomes insignificant, and relative to #t^3#, #t^2# becomes insignificant.

That means:

#color(blue)(lim_(t->oo) (t^2 + cancel(2)^"small")/(t^3 + cancel(t^2 + 1)^"small"))#

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

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

#= color(blue)(0)#

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