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lim as t approaches infinity (t^2 + 2)/(t^3 + t^2 -1)? Would this be 0? Could you show...

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carrawaych | Student, Undergraduate | (Level 1) Honors

Posted April 15, 2013 at 6:08 PM via web

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lim as t approaches infinity (t^2 + 2)/(t^3 + t^2 -1)?

Would this be 0? Could you show me step by step. I believe we need to divid both top and bottom by the highest power which would be t^3???

 

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted April 15, 2013 at 6:15 PM (Answer #1)

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`lim_(xrarroo) (t^2 + 2)/(t^3 + t^2 -1)`

`= lim_(xrarroo) (t^3(1/t+2/t^2))/((t^3(1+1/t-1/t^3)))`

`= lim_(xrarroo) (1/t+2/t^2)/(1+1/t-1/t^3)`

`= (1/oo+2/oo)/(1+1/oo-1/oo)`

`= (0+0)/(1+0+0)`

`= 0`

 

So the answer is 0.

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oldnick | (Level 1) Valedictorian

Posted April 16, 2013 at 2:29 AM (Answer #2)

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

 

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

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