`lim_(x-> oo) (x^2 + 2)/(x - 1)` Find the limit, if possible

Textbook Question

Chapter 3, 3.5 - Problem 15c - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

Posted on

`lim x->oo (x^2 + 2)/(x-1)`

`or, lim x->oo (2x)/1`

`or, lim x-> (2x) = oo`

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scisser | (Level 3) Honors

Posted on

Plug in `oo ` everywhere you have x
`lim_(x->oo)(oo^2+2)/(oo-1)=oo/oo `

Since you have , you can use L^Hopital's Rule and differentiate the numerator and denominator independently.

`lim_(x->oo)2x=oo `

Therefore,

the `lim_(x->oo)(x^2+2)/(x-1)=oo `

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