What is the limit of #[ ( t^2 + 2) / (t^3 + t^2 -1) ]# as x approaches negative infinity?

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Answer 1 · 2017-10-29T19:59:39

#0#

Lets let # f(t) = (t^2+2)/(t^3+t^2-1)#

Can we write as #lim_(x->-oo) f(t)#

As; #lim_(x->-oo) (1/t+2/t^3)/(1+1/t-1/t^3)#,
By dividing both the numorator and denominator by #t^3#

as #x to -oo#; #1/t +2/t^3 to 0#

as #x to -oo#; #1+1/t-1/t^3 to 1#

Hence #lim_(x to -oo) f(t) = 0/1#

#=0#