`lim_(x -> oo) x/(x^2 + 3)` Find the limit.

Textbook Question

Chapter 3, 3.5 - Problem 23 - Calculus of a Single Variable (10th Edition, Ron Larson).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

Posted on

Divide both numerator and denominator by x:

`x/(x^2+3) = 1/(x+3/x)` .

When `x -> oo,` `3/x -> 0` and the limit is `1/(oo + 0) = 1/oo ` = 0.

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scisser | (Level 3) Honors

Posted on

Plug in ` ` `oo` everywhere for x

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

` `

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

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

1 divided by a really big number is simply 0.

Therefore,

the `lim_(x->oo)x/(x^2+3)=0 `

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