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

Textbook Question

Chapter 3, 3.5 - Problem 16b - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

`limx->oo (3-2x)/(3x-1)`

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

`or, limx->oo (0-2)/(3-0) = -2/3`

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scisser | (Level 3) Honors

Posted on

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

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

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

Therefore,

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

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