Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

limit: [(12x)/(9-8x)] as x --> (+)9/8 and (-)9/8. I am confused how to do this. L'hospital, substitution and conjugates will not solve this as they result in the division of zero. I tried factoring out the largest degree:

(x/x)(12/[9/x]-8)

integer over variable results in 0:

12/ (0 - 8) =

12/-8 =

-3/2

However, upon further investigation this is the limit as it approaches infinity. I have tried a few other things, but none have resulted in a correct answer, this is as close as I have gotten. What do I have to do to get x --> (+)9/8 instead of x --> (+)inf? Thanks.

share|improve this question
    
Using wolfram|alpha I obtained the correct solutions: (-)infinity, (+)infnity; respectively for +9/8 and -9/8. However, I still do not understand how to obtain this solution algebraically? –  Mr_CryptoPrime Feb 16 '11 at 9:22
    
Just look at what happens when $x \to \frac{9}{8}+$. The denominator $\to 0$ and hence it goes to $-\infty$. –  anonymous Feb 16 '11 at 9:26
    
Yes, I understand now...thanks both of you! :) –  Mr_CryptoPrime Feb 16 '11 at 9:29

1 Answer 1

up vote 2 down vote accepted

If the limit of the denominator is 0 and the limit of the numerator is nonzero, the limit does not exist (is $\pm\infty$). You can easily determine the sign by plugging in numbers close to $\frac{9}{8}$ on either side.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.