# Tutor.com Limits Session

##### Sep. 9, 2013

Session Transcript - Math - Calculus, 9/3/2013 9:33PM - Tutor.comSession Date: 9/3/2013 9:33PM
Length: 39.4 minute(s)
Subject: Math - Calculus

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

[00:00:00] Limits

Crystal D (Tutor)
[00:00:15] Good Evening!

[00:00:09] hello
[00:01:01] determine the limit, write a simpler function

Crystal D (Tutor)
[00:01:55] Yes I can.

[00:03:04] just all around
[00:03:06] solving it

Crystal D (Tutor)
[00:03:26] Ok. Ready to get started!
[00:03:28] ?

[00:03:52] yes!

Crystal D (Tutor)
[00:05:05] So, to be able to do part a, we need to simplify g(x)

[00:05:30] this is where im stuck

Crystal D (Tutor)
[00:06:20] I cannot see anything you are writing if you are writing anything new

[00:06:34] no i am not, sorry

Crystal D (Tutor)
[00:06:43] Thats alright,
[00:07:22] Ok. I'm going to write on a new whiteboard

[00:07:33] alright!

Crystal D (Tutor)
[00:08:19] To simplify this, we need to move some things around. The first thing we are going to do is change the top of the fraction a bit
[00:08:46] To start, we are going to "pull" an x out to get a similar equation that means the same thing
[00:09:11] Does that make sense?

[00:09:18] yes

Crystal D (Tutor)
[00:09:23] Great!
[00:09:56] Next thing is to factor the x^2-1. Because it is a perfect square, factoring it is simple.
[00:11:29] What you just wrote is the reason why we are doing this. Now, when we find the two different limits and plug in 1 and -1, we wont get 0 on the bottom of a fraction
[00:12:10] Do you remember how to do limits?

[00:12:27] just plug in?
[00:12:33] 2 and 0

Crystal D (Tutor)
[00:12:59] There you go!
[00:13:10] You got it!

[00:13:32] awesome, could u help me one laston? ill work it, and you tell me if i mess up?

Crystal D (Tutor)
[00:13:48] Is it the same type of problem?

[00:13:53] yes

Crystal D (Tutor)
[00:14:12] Then sure, go right ahead!

[00:14:44] right?

Crystal D (Tutor)
[00:14:56] Yes!
[00:15:32] You got it!

[00:15:42] one more?
[00:15:48] if u have time

Crystal D (Tutor)
[00:16:20] Sure, no problem. I have about 10 minutes if you want to keep going on the same types of problems.
[00:17:08] You got it!

[00:18:14] ohhhh, help?
[00:18:25] i got it
[00:18:37] ?

Crystal D (Tutor)
[00:18:47] Great job!

[00:19:31] one last one, this looks hard

Crystal D (Tutor)
[00:21:01] Give me one minute to solve it out. While I'm doing that, think about how you can simplify this to make it look nicer.

[00:21:13] alrighty!
[00:23:07] i got nothing, not understanding it :(

Crystal D (Tutor)
[00:23:39] thats alright! do you remember anything about the word conjugate?

[00:23:58] i recall it
[00:24:05] somewhat...

Crystal D (Tutor)
[00:24:17] Do you remember what you do for it?

[00:24:24] no....

Crystal D (Tutor)
[00:25:32] No problem. What the conjugate says is that we can multiply the top and bottom by the opposite (meaning positive if negative and negative if positive) of the top of the fraction
[00:25:36] So it looks like this....

[00:26:37] ahhhhh yes, i remember it now!

Crystal D (Tutor)
[00:27:02] Great! Why dont you try solving it from here?

[00:27:51] ?

Crystal D (Tutor)
[00:28:46] Very good on the bottom. For the top, remember, when you multiply two square roots that are the same, all that is left is what was under the square root. You did not need to square the x+5

[00:29:04] ohhh yes!
[00:29:15] ?

Crystal D (Tutor)
[00:29:34] Good job!
[00:30:38] Then all you need to do is either simplify, or you can just plug in 4 to get your answer.

[00:30:56] how do i. simplify thus
[00:32:11] thats all?

Crystal D (Tutor)
[00:32:21] Give me one minute

[00:33:04] alright, and if i try to plug in 4 on top t results in 0

Crystal D (Tutor)
[00:34:47] I figured out why it was not really working for us. When we multiplied the bottom, we did not FOIL it. I am going to continue on a new whiteboard

[00:35:03] ahhhh, thanks!

Crystal D (Tutor)
[00:37:14] I apologize, we can actually just cancel the (x-4)
[00:37:18] right away
[00:37:49] There we go!
[00:37:51] Whew!
[00:38:01] Does that make sense?

[00:38:10] ohhhh, 1 question, how did u get the x-4 on top?
[00:38:21] ohhh got it

Crystal D (Tutor)
[00:38:36] Great!

[00:38:44] i understand it! THANKS!

Crystal D (Tutor)
[00:38:51] Well, do you have any questions about what we did today?