`lim_(x-> oo) (3 - 2x)/(3x^3 - 1)` Find the limit, if possible

Textbook Question

Chapter 3, 3.5 - Problem 16a - Calculus of a Single Variable (10th Edition, Ron Larson).
See all solutions for this textbook.

2 Answers | Add Yours

hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

`lim x->oo (3-2x)/(3x^3 - 1)`

`or, lim x->oo {(3/x^3) - ((2x)/(x^3))}/{((3x^3)/(x^3))-(1/x^3)}`

`or, lim x->oo {(3/x^3)-(2/x^2)}/{3-(1/x^3)} = (0-0)/(3-0) = 0`

``

` `

scisser's profile pic

scisser | (Level 3) Honors

Posted on

Plug in `oo ` everywhere you have x
`lim_(x->oo)(3-2(oo))/(3(oo^3)-1)=oo/oo `

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

`lim_(x->oo)-2/(9x^2)=-2/oo `

-2 divided by a really big number will just be 0.

Therefore,

the `lim_(x->oo)(3-2x)/(3x^3-1)=0 `

We’ve answered 318,916 questions. We can answer yours, too.

Ask a question