find the limit of (x+1)/(3x-2)find the limit of lim x->-infinity (x+1)/(3x-2)

Expert Answers
lfryerda eNotes educator| Certified Educator

We need to factor out the x terms from the numerator and the denominator, but first do a transformation from negative to positive infinity.

Let `u=-x`

Then `u->infty` as `x->-infty` .


`=lim_{u->infty}{-u+1}/{-3u-2}`    factor out the u


`=lim_{u->infty}{-1+1/u}/{-3-2/u}`   now take limits



The limit is `1/3`

embizze eNotes educator| Certified Educator

Find the limit as x decreases without bound of `f(x)=(x+1)/(3x-2)` :


If we try direct substitution we get the form `(-oo)/(-oo)`

Apply L'hopital's rule: `lim (f(x))/(g(x))=lim(f'(x))/(g'(x))` :