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

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hkj1385 eNotes educator| Certified Educator

`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`

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scisser | Student

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`

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