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

Answer 1

Paisley Johnson

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^-#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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

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