thinay Posts: 40, Reputation: 2 Junior Member #1 Jul 13, 2009, 05:58 AM
Topic: infinite limits
Can anyone help me with this problem. :)

The given is: g(x) = x/(x-5) and I need to find the vertical asymptote of the graph of g and the sketch of the graph of g for values close to the asymptote.

Here is how I solved it.
g(x) = x/(x-5)
x->5
= (lim x) / (lim x - lim 5)
x->5 x->5
= 5/(5-5)
= 5/0
= positive infinity

I don't know if my answer is correct but I tried my best to answer it. I don't have a graph yet. :(

I hope you can help me with this. Thanks in advance! :)
 Unknown008 Posts: 8,076, Reputation: 723 Uber Member #2 Jul 13, 2009, 06:14 AM

You have to find at which value of x does g(x) equals to positive infinity. That value is the line where you have the vertical asymptote.

The graphing should be quite easy.
 thinay Posts: 40, Reputation: 2 Junior Member #3 Jul 13, 2009, 06:25 AM

Wait. I want to know first if my answer 5/0 = positive infinity correct? :)
 Unknown008 Posts: 8,076, Reputation: 723 Uber Member #4 Jul 13, 2009, 06:28 AM

Yup, so what you think the value of x is? (you already got that! ;))
 thinay Posts: 40, Reputation: 2 Junior Member #5 Jul 13, 2009, 06:32 AM

Is x=5?? :D
 Unknown008 Posts: 8,076, Reputation: 723 Uber Member #6 Jul 13, 2009, 06:34 AM

YES!! Congrats! :)
 thinay Posts: 40, Reputation: 2 Junior Member #7 Jul 13, 2009, 06:43 AM

Thank you for your help! Clap! Clap! Clap! :D

wait. To get the values close to the asymptote.. Am I just going to substitute the value of x..

example: g(x) = (5.01)/(5.01-5)
is this correct? :) or not? :(
 Unknown008 Posts: 8,076, Reputation: 723 Uber Member #8 Jul 13, 2009, 06:52 AM

You can do that. However, if you're plotting, that might be somewhat difficult.

If you did the $\frac{5.01}{5.01-5}$, that gives 501. Some larger numbers may perhaps be more practical. Still, I don't know how you do in your country to do such numbers, but you'll see that the graph decreases very fast, then it becomes more horizontal around x=8
 thinay Posts: 40, Reputation: 2 Junior Member #9 Jul 13, 2009, 06:59 AM

Oh! I see. Thanks a lot! :D
 Unknown008 Posts: 8,076, Reputation: 723 Uber Member #10 Jul 13, 2009, 07:03 AM

And you can try plotting the part to the right of the asymptote. You'll get something that you have perhaps never seen when you go to the negative values of x.
 thinay Posts: 40, Reputation: 2 Junior Member #11 Jul 13, 2009, 07:14 AM

Ok! Ok! I'll do that. :)

Hey! :D What do you think in this problem? Is it positive or negative infinity?
lim (x/x+2) + (1/x^2-4)
x->-2^+

when I tried to answer it. I end with + infinity.
 thinay Posts: 40, Reputation: 2 Junior Member #12 Jul 13, 2009, 07:21 AM

Ok! Ok! I'll do that. :)

Hey! :D What do you think in this problem? Is it positive or negative infinity?
lim (x/x+2) + (1/x^2-4)
x->-2^+

when I tried to answer it. I end with + infinity.
 thinay Posts: 40, Reputation: 2 Junior Member #13 Jul 13, 2009, 07:26 AM

It should be - infinity..
 Unknown008 Posts: 8,076, Reputation: 723 Uber Member #14 Jul 13, 2009, 07:28 AM

Wait a sec. Does that mean you and akotoh are the same person? I've seen the exact question on another recent thread :confused:

Anyway, the question just got answered.
 thinay Posts: 40, Reputation: 2 Junior Member #15 Jul 13, 2009, 07:40 AM

Nope! I have read his/her post and I'm just confused what really the answer is. Because the other one says that the answer is - and the other says that its +.
That's it! :)
 Unknown008 Posts: 8,076, Reputation: 723 Uber Member #16 Jul 13, 2009, 07:46 AM

Just had the graph plotted. It goes to -ve infinity, with asymptote at x = -2.
 thinay Posts: 40, Reputation: 2 Junior Member #17 Jul 13, 2009, 07:58 AM

Hey! I've tried to substitute the value of x to g(x)= x/(x-5)..

if..
g(6) = 6
g(7) = 3.5
g(8) = 2.67
g(9) = 2.25
g(10) = 2

am I correct? :D
 Unknown008 Posts: 8,076, Reputation: 723 Uber Member #18 Jul 13, 2009, 08:00 AM

Yup! :)
 thinay Posts: 40, Reputation: 2 Junior Member #19 Jul 13, 2009, 08:05 AM

Okey! I'm totally done! :D
Thank you very much for your help!

I need to sleep now. Its already 11pm here in our country.

Hope you can help me again next time! Thanks! More powers! ;)
 Unknown008 Posts: 8,076, Reputation: 723 Uber Member #20 Jul 13, 2009, 08:07 AM

Ok, Good night! :)

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