# 3 Questions (Limits)

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• Mar 14th 2007, 09:46 AM
SportfreundeKeaneKent
3 Questions (Limits)
Here are three questions which I'm trying to solve. The first one I solved but was hoping someone could verify because I'm not sure that the solution is right. The 3rd one I need help on because I can't factor out or cancel anything.

http://img126.imageshack.us/img126/2...answersyt0.png

Link to image:

http://img126.imageshack.us/img126/2...answersyt0.png
• Mar 14th 2007, 09:56 AM
ThePerfectHacker
The first 1 you can substitute.

The third one you get (SOMETHING)/0 where SOMETHING
not = zero. Thus it is + infinity.

The second one you get 0/0 which is bad.
You factor,

x^3-3x^2+4
x^3-2x^2+4-x^2
x^2(x-2)+(2-x)(2+x)
x^2(x-2)-(x-2)(x+2)
(x-2)(x^2-x-2)

Now you can cancel (x-2) to get,

x^2-x-2 and take limit as x -- > 0
• Mar 14th 2007, 10:17 AM
frenzy
for #3 the limit does not exist. ( it is not +\infty)
• Mar 14th 2007, 06:29 PM
SportfreundeKeaneKent
So you can substitute in the first one and say that it approaches 0 when you substitute it gives 0/3 which equals 0?

And I still don't understand the 3rd one. Is there a way to actually show if it's approaching + or - infinity?
• Mar 14th 2007, 06:39 PM
frenzy
Quote:

Originally Posted by SportfreundeKeaneKent
So you can substitute in the first one and say that it approaches 0 when you substitute it gives 0/3 which equals 0?

And I still don't understand the 3rd one. Is there a way to actually show if it's approaching + or - infinity?

Look at the left and right hand limits.

(graph it or look at numerical values if you want)

comming from the right the limit + infinity

comming from the left the limit is - infinity

therefore the limit doesn't exist.