`lim_(x -> oo) (2x - 1)/(3x + 2)` Find the limit.

Textbook Question

Chapter 3, 3.5 - Problem 21 - 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) (2x-1)/(3x+2)`

`or, lim_(x->oo) {((2x)/x)-(1/x)}/{((3x)/x)+(2/x)}`

`or, lim_(x->oo) (2-(1/x))/(3+(2/x)) = (2-0)/(3+0) = 2/3`

``

scisser's profile pic

scisser | (Level 3) Honors

Posted on

Use L ^ Hopital's Rule:

`lim_(x->oo)(2x-1)/(3x+2)`

Under LH, taking the derivative of the numerator and denominator independently.

`lim_(x->oo)2/3 `

Therefore, the `lim_(x->oo)(2x-1)/(3x+2) =2/3`

We’ve answered 318,928 questions. We can answer yours, too.

Ask a question