# Tutor.com Limits Session

##### Nov. 6, 2012

Session Transcript - Math - Calculus, 11/4/2012 7:24PM - Tutor.comSession Date: 11/4/2012 7:24PM
Length: 44.6 minute(s)
Subject: Math - Calculus

System Message
[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)

William R (Tutor)
[00:00:11] Hi there!

Guest (Customer)
[00:00:25] File Shared > Calculus Classwork 2.doc

System Message

Guest (Customer)
[00:00:59] i need help on that

William R (Tutor)
[00:01:07] Ok, I did get the file.
[00:01:17] Let's put the first one on the board.

Guest (Customer)
[00:01:23] i did the first one
[00:01:30] i need help on 12

William R (Tutor)
[00:02:25] Oh, ok.
[00:03:41] So the idea behind the first one and number 12 are very similar. What did you do for the first?

Guest (Customer)
[00:04:04] u plugged it into the calculator
[00:04:31] plugged in the x values for -2,- 1,0,0.5,1,1.5,2,3

William R (Tutor)
[00:04:58] Why did you choose those particular values?

Guest (Customer)
[00:05:58] idk
[00:06:08] my last tutor just told me those were okay

William R (Tutor)
[00:06:19] Well, keep in mind what a limit is trying to tell you.
[00:06:36] For your first problem, the limit was approaching the x-value of 1.

Guest (Customer)
[00:07:01] ya

William R (Tutor)
[00:07:33] The function you were given was (x-2)/(x^2+x-6).
[00:08:14] So the limit tells you to figure out the value you would get from that function you were given as you get progressively closer to the x-value of 1.

Guest (Customer)
[00:08:38] tya
[00:09:44] so what?

William R (Tutor)
[00:09:49] So for that problem, you would want to plug in values like .5, .9, .99, and so on into the function given because those are all less than 1 but keep getting close to 1.
[00:10:07] Likewise, use values that are a bit bigger than 1, like 1.5, 1.1, 1.01, and so on.
[00:10:17] Those values would be more appropriate, really.

Guest (Customer)
[00:10:31] my last tutor told me any values would be fine

William R (Tutor)
[00:10:39] That's not really true, though.

Guest (Customer)
[00:10:53] as long as the two other values closest to 1 would be really close like .5 and 1.5

William R (Tutor)
[00:11:00] Those values aren't really very close to the x-value that the limit was supposed to approach.

Guest (Customer)
[00:11:02] which is 1 above 1 and and 1 below 1

William R (Tutor)
[00:11:20] Even .5 and 1.5 aren't very good because they're fairly far from 1, relatively speaking.
[00:11:42] .9, .99, .999, and so on are much closer to 1 than .5 is, for example.
[00:12:01] Likewise, 1.1, 1.01, 1.001, and so on is bigger than 1, but those values continue to get closer and closer to 1.

Guest (Customer)
[00:12:10] so then how would u know which ones are godo then

William R (Tutor)
[00:12:10] So those would be much more appropriate.

Guest (Customer)
[00:12:12] good*

William R (Tutor)
[00:12:45] Well, you want to use values very close to the x-value that the limit tells you that you should approach.
[00:12:58] For the limit on the board, use x-values very close to -2.
[00:13:09] For example, use -2.1, -2.01, -2.001, and so on.

Guest (Customer)
[00:13:19] so just keep adding a 0?

William R (Tutor)
[00:13:25] Right!

Guest (Customer)
[00:13:37] si us tgat for
[00:13:47] so is that for above the appraching x value or below

William R (Tutor)
[00:13:49] Because the difference between the values we're using to approximate the limit and the actual value for the limit keeps getting smaller.
[00:15:14] Likewise, you could try -1.9, -1.99, and so on.

Guest (Customer)
[00:16:23] oh k

William R (Tutor)
[00:16:31] Do you see why those are much better to use than values like what you had been trying?

Guest (Customer)
[00:16:41] yeah
[00:16:47] but that would get confusign for me
[00:16:50] which ones are smaller
[00:16:54] and which ones are bigger

William R (Tutor)
[00:17:48] You can use a number line, like what I drew on the board.
[00:18:00] -2.1 is "more negative" than -2, so it is a smaller number.

Guest (Customer)
[00:18:18] oh k

William R (Tutor)
[00:18:55] So are you okay making a table with those values now?

Guest (Customer)
[00:20:19] so like this
[00:20:23] -2.001
[00:20:26] -2.01
[00:20:28] -2.1
[00:20:31] -2
[00:20:38] -1.999
[00:20:41] 1.99
[00:20:44] 1.9
[00:20:50] sorry add negative to the last two

William R (Tutor)
[00:20:54] You don't want to use -2 itself, since that would give you 0/0 in this problem, but you have the right idea!
[00:21:13] Just plug each of those into your function to get your table, and you're set!

Guest (Customer)
[00:21:44] and what would be the limit be then?

William R (Tutor)
[00:22:08] Do you have a graphing calculator?
[00:22:16] Or something else that would enable you to graph this function?

Guest (Customer)
[00:22:22] ya

William R (Tutor)
[00:22:47] Ok, so try graphing this function first.
[00:23:01] Then, get really close to x=-2 and see what the corresponding y-value appears to be.

Guest (Customer)
[00:23:44] oh

William R (Tutor)
[00:23:55] So what will you get here?
[00:24:54] Any ideas?

Guest (Customer)
[00:26:02] for -2 it says error

William R (Tutor)
[00:26:09] It will, yep.

Guest (Customer)
[00:26:09] but -2.1 says 12.61
[00:26:21] and -1.999 says 11.994

William R (Tutor)
[00:26:26] Good!

Guest (Customer)
[00:26:33] so it would be 12?

William R (Tutor)
[00:26:33] So what value does it appear to be getting close to?

Guest (Customer)
[00:26:49] 12

William R (Tutor)
[00:26:56] Exactly!
[00:27:31] And that means 12 is the value of the limit you were looking to evaluate.

Guest (Customer)
[00:27:46] so 12 is the limit

William R (Tutor)
[00:27:53] You bet!

Guest (Customer)
[00:28:03] bc at the when the value appraches x the y value is 12

William R (Tutor)
[00:28:09] Your teacher will go through some other techniques soon to show you how that value is obtained exactly, I'm sure.
[00:28:22] That's exactly the idea of a limit.
[00:28:33] And that's what these problems your teacher gave you are attempting to show you.
[00:28:45] Does that make sense?

Guest (Customer)
[00:29:17] oh i c
[00:29:18] a bit
[00:29:28] so would the x values i showed u be okay?

William R (Tutor)
[00:29:34] Yep, absolutely.
[00:29:53] I think your teacher would be pretty happy with them since they help to show that you understand the idea of a limit.

Guest (Customer)
[00:30:28] well wat about the graph

William R (Tutor)
[00:30:43] Well, you got those values by using your calculator, right?

Guest (Customer)
[00:30:47] and at -2 what would i do?
[00:30:52] ya

William R (Tutor)
[00:31:09] Using your calculator is what the directions meant when they said to use a graphing utility.

Guest (Customer)
[00:31:22] so would i have to sketch it?

William R (Tutor)
[00:31:38] At x=-2, you found it gave an error, and that's going to be a kind of problem that is beyond the scope of the problem you were given.
[00:31:59] If you're doing approximations to limits, you should be working up to how to evaluate limits exactly pretty soon.

Guest (Customer)
[00:32:07] so wat would i do there just leave it blank ?

William R (Tutor)
[00:32:12] You shouldn't need to sketch it since the directions didn't state that you need to do that.

Guest (Customer)
[00:32:35] but it says use a graphing utility to graph the solution

William R (Tutor)
[00:32:46] No, it just said to use a graphing utility to look at the graph and confirm the result you came up with.

Guest (Customer)
[00:32:54] graph the function to comfirm your result*

William R (Tutor)
[00:32:56] You can always graph it, sure!
[00:33:09] But it's only asking you to look at the graph really.

Guest (Customer)
[00:33:15] but it says we have to right

William R (Tutor)
[00:33:24] No.
[00:33:32] It says to graph it on your graphing utility.
[00:33:44] If you'd like to graph it on your paper to be safe, you can do so, certainly.
[00:34:23] But it's asking you to evaluate using the table, the way you've already done, to determine that the limit turned out to be 12.

Guest (Customer)
[00:34:51] so how would u evalute using the table?

William R (Tutor)
[00:34:55] And then just to look at the graph and see that the y-value is pretty close to 12 the closer you get to the x-value of -2.
[00:35:04] You've already done that, don't forget!
[00:35:12] You plugged values in earlier.
[00:35:40] Those are the values you need for your table.

Guest (Customer)
[00:36:42] i get a parabola when i graph it tho

William R (Tutor)
[00:37:01] That's not a problem. It's what you should get, actually.
[00:37:16] You've completed the problem at this point, but if you have further questions about it, I can transfer you to another tutor.

Guest (Customer)
[00:37:16] but it doesnt show the curve at -2
[00:37:24] or at 12

William R (Tutor)
[00:37:26] I'm at the end of my shift, however.

Guest (Customer)
[00:37:29] it just stops at 10

William R (Tutor)
[00:38:05] You may not have a viewing window large enough to see the entire graph, so you'll have to zoom out a bit to get more of the graph on your screen.
[00:38:17] Would you like me to transfer you to another tutor to continue working on this problem?

Guest (Customer)
[00:38:39] sure
[00:38:43] and thanks

William R (Tutor)
[00:38:53] Ok, give me just a moment.
[00:38:56] Have a great evening!

Guest (Customer)
[00:39:06] u too
[00:39:09] bye thnmnx

William R (Tutor)
[00:39:27] You're welcome!
[00:40:53] Just a moment, it appears that I've lost the button to transfer.

Guest (Customer)
[00:41:25] k

William R (Tutor)
[00:41:36] It appears that the option to transfer expires after the first 10 minutes of our session, which is why I've lost that option.
[00:41:48] You have completed this problem, however.

Guest (Customer)
[00:41:51]
[00:41:55] so u lied to me

William R (Tutor)
[00:42:06] I did not, no.
[00:42:19] I didn't realize that the option to transfer would fail after that time period.

Guest (Customer)
[00:42:20] u said u would transfer me to another tutor
[00:42:24] which u did not

William R (Tutor)
[00:42:31] I'm sorry, but I don't have that option anymore.

Guest (Customer)
[00:42:36] shame on you shame on your whole family, you lie you lie

William R (Tutor)

Guest (Customer)
[00:42:49] lmaooo im joking sorry lol
[00:43:04] ik i understand and i thought it was expired already

William R (Tutor)
[00:43:14] Oh, I see.
[00:43:30] Well, I would recommend continuing to work on this problem using the information we've already discussed.
[00:43:51] You have all the tools you need, but if you have further questions, you can always reconnect to another tutor.

Guest (Customer)
[00:44:17] ok
[00:44:18] thanks bye

William R (Tutor)
[00:44:29] You're welcome! Have a good evening.