Tutor.com Infinite Series, Taylor Series Session

May. 3, 2016

  • Poor
  • Fair
  • Average
  • Good
  • Excellent
  • Click to rate this Poor
  • Click to rate this Fair
  • Click to rate this Average
  • Click to rate this Good
  • Click to rate this Excellent


Session Transcript - Math - Calculus, 4/26/2016 5:49PM - Tutor.com
Session Date: 4/26/2016 5:49PM ET
Length: 44.8 minute(s)
Subject: Math - Calculus

Print Transcript
Replay Session

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

Guest (Customer)
[00:00:00] Hi, I need help with these problems. [ File > http://lhh.tutor.com/SharedSessionFiles/6c98f7ec-4419-4df4-a6e7-afa0ba96a812_Screen_Shot_2016-04-26_at_5.22.07_PM.png ]

Lucia F (Tutor)
[00:00:12] Welcome! Let's get started.
[00:00:19] Give me a minute while I look at your problem

Guest (Customer)
[00:00:34] hi! okay no problem

Lucia F (Tutor)
[00:03:00] I'm working on this...
[00:03:08] Alright
[00:03:13] Do you know how to start this problem?

Guest (Customer)
[00:03:20] i started the first one but i am stuck
[00:03:38] i'll show you how far i got

Lucia F (Tutor)
[00:04:01] Okay!
[00:04:10] Oh sorry, added the image in the middle of your writing!

Guest (Customer)
[00:04:47] now i am not sure what to do

Lucia F (Tutor)
[00:05:25] What method did you use to try and find the interval of convergence? What does that formula account for?

Guest (Customer)
[00:05:41] i used the ratio test
[00:05:52] i am stuck i have no idea how to do this
[00:05:59] like how to find the interval of convergence

Lucia F (Tutor)
[00:06:09] Okay, let's work on it togheter
[00:06:40] So you have to find the interval of conevrgence and tried the radio test... Let me check the formula you got is right

Guest (Customer)
[00:06:45] ok

Lucia F (Tutor)
[00:08:11] Can I ask why you took the absolute value of x?

Guest (Customer)
[00:08:38] because the ratio test is the lim as n approaches infinity of the absolute value of an+1/an

Lucia F (Tutor)
[00:09:11] Oh, you're right I forgot that one detail of the absolute value in the ratio test
[00:09:23] Ok, so you got the limit in the ratio test is the absolute value of x
[00:09:38] and what does the ratio test tell you about convergence?

Guest (Customer)
[00:09:54] i don't know, i'm confused

Lucia F (Tutor)
[00:10:45] That's alright Do you know how to use the ratio test? When does it say the series converges?

Guest (Customer)
[00:11:00] no idea haha

Lucia F (Tutor)
[00:11:26] Alright, let's start from there!
[00:11:33] Like you said, the radio test is this...
[00:12:15] You know that definition, right?

Guest (Customer)
[00:12:28] yes

Lucia F (Tutor)
[00:12:41] When L < 1, the infinite sum for an convernges
[00:12:54] when L > 1, the infinite sum for a_n diverges
[00:12:56] correct?

Guest (Customer)
[00:13:06] yes

Lucia F (Tutor)
[00:13:34] And you got |x| for the series in your problem
[00:13:48] How can you use that to find out where is diverges and where it converges?

Guest (Customer)
[00:14:29] i don't know

Lucia F (Tutor)
[00:15:10] I'm sure you can do it Tell me again, when you use the ratio test, you know the series converges when you get what kind of number?

Guest (Customer)
[00:15:23] one that is less than 1

Lucia F (Tutor)
[00:15:42] Good! And for the series you want to test, what did you get?

Guest (Customer)
[00:15:49] x

Lucia F (Tutor)
[00:16:18] Great! so if you wanted the series to converge, what would x have to be?
[00:16:22] |x|*

Guest (Customer)
[00:16:32] less than 1?

Lucia F (Tutor)
[00:16:39] Excellent!
[00:17:06] Do you see now the condition you got for x?

Guest (Customer)
[00:17:11] yes
[00:17:16] so what is the interval?

Lucia F (Tutor)
[00:17:19] That's a first step towards the inteval of convergence
[00:17:38] well, if it has to be |x| < 1, what would x be between?

Guest (Customer)
[00:18:02] from -1 to 1

Lucia F (Tutor)
[00:18:07] Good job!

Guest (Customer)
[00:18:18] but how do we know whether each of those values is included or excluded
[00:18:28] like when we write it, if it has a parentheses or bracket

Lucia F (Tutor)
[00:19:04] What has to have parentheses or brackets? I don't understand, sorry

Guest (Customer)
[00:19:20] if it's (-1, 1] or (-1,1) or [-1,1] etc

Lucia F (Tutor)
[00:19:27] Oh!
[00:20:03] Well, you know from the ratio test that if L is exactly 1 then the test is not useful, right? L has to be exactly less than 1
[00:20:16] so if |x| has to be exactly less than one...
[00:20:34] what would that mean, say for positive x's?

Guest (Customer)
[00:20:58] they have to be less than 1?

Lucia F (Tutor)
[00:21:24] That's right, does that mean they can be 1?

Guest (Customer)
[00:21:36] no

Lucia F (Tutor)
[00:21:56] Great! So would you use parenthesis or brackets for 1 in the interval?

Guest (Customer)
[00:22:11] which one means what?

Lucia F (Tutor)
[00:22:38] Parenthesis means it's not part of the interval, bracket means it is

Guest (Customer)
[00:22:47] so then it will be parenthesis

Lucia F (Tutor)
[00:22:54] Great job!

Guest (Customer)
[00:23:07] so [-1, 1)?

Lucia F (Tutor)
[00:23:39] The -1 is the same. Do you know how to evaluate inequalities iwth absolute values?
[00:23:48] I can show you how

Guest (Customer)
[00:24:27] no

Lucia F (Tutor)
[00:24:59] Alright, let me show you quickly how to do them
[00:25:09] Let's do the same as this example
[00:25:30] You have to divide it in two.. One for positive x's ....
[00:25:56] Which means the absolute value remains the same, since it's already positive
[00:26:06] And one for negative values...
[00:26:38] When you remove the absolute value bars from a negative unknown number (any negative x) you add a minus sign in front of it
[00:26:51] That way, x becomes positive!

Guest (Customer)
[00:26:54] ok

Lucia F (Tutor)
[00:27:25] Now, how do you clear out the x in the negative one?

Guest (Customer)
[00:27:36] divide by negative 1

Lucia F (Tutor)
[00:27:56] Good! and what happens? You have to be careful with that step

Guest (Customer)
[00:28:04] inequality flips

Lucia F (Tutor)
[00:28:09] Excellent!!
[00:28:24] And you get this, is that right?

Guest (Customer)
[00:28:29] yes

Lucia F (Tutor)
[00:28:49] No it's not haahah I wrote the inequality sign wrong, sorry

Guest (Customer)
[00:29:01] oops haha

Lucia F (Tutor)
[00:29:11] Very well
[00:29:18] So what is the resulting interval from this?

Guest (Customer)
[00:29:26] [-1,1]?

Lucia F (Tutor)
[00:29:47] That's almost right! Remember they are not included!

Guest (Customer)
[00:29:56] (-1,1)?

Lucia F (Tutor)
[00:30:03] If they were included, the inequality sign would be this:
[00:30:11] Correct!

Guest (Customer)
[00:30:20] yay

Lucia F (Tutor)
[00:30:33] those I wrote on the board, with an extra line, mean less than or equal to, and greater than or equal two

Guest (Customer)
[00:30:38] yes

Lucia F (Tutor)
[00:30:39] they are different
[00:30:44] Great!
[00:30:59] Only when they can be equal to that you use brackets
[00:31:14] Alright then, want to try the next problem and see if you got the concepts right?

Guest (Customer)
[00:31:29] yes i actually tried it already and wanted to check it with you

Lucia F (Tutor)
[00:31:42] Good! Let's see then

Guest (Customer)
[00:32:12] i'm going to show you the final steps because the earlier ones are all just rearrangement

Lucia F (Tutor)
[00:32:39] Okay!

Guest (Customer)
[00:33:44] tell me if that's right

Lucia F (Tutor)
[00:34:22] The answer you got is correct! But remember to not omit terms when writing the limits since teacher don't normally like that in exams

Guest (Customer)
[00:34:37] like which terms?

Lucia F (Tutor)
[00:34:59] Here, you didn't keep writing the |x|

Guest (Customer)
[00:35:03] right

Lucia F (Tutor)
[00:35:17] Even though it's right the limit of the following part is 1
[00:35:24] But What you get is |x| as the result
[00:35:32] and that is what has to be less than one
[00:35:51] It's a common thing students don't think they have to write and teachers don't like it
[00:36:16] Alright, so did you understand everything we did to get the interval of convergence?
[00:36:32] Can you write down the final result for that one as an interval too?

Guest (Customer)
[00:37:46] (-1,1)?

Lucia F (Tutor)
[00:37:52] Great!!
[00:37:58] You did really well!

Guest (Customer)
[00:38:11] thank you

Lucia F (Tutor)
[00:38:35] Was everything we did clear to you? Do you need help with anything else?

Guest (Customer)
[00:40:32] yes i need help with one more thing that i am stuck with relating to this
[00:40:46] it's a different problem but i am having trouble with the final inequality that i got

Lucia F (Tutor)
[00:41:06] Okay, let's see it!

Guest (Customer)
[00:42:09] is that right??
[00:42:24] because one of my friends got (-1,5) instead of (-5, 5)

Lucia F (Tutor)
[00:42:31] The one on the left yes, it's right
[00:42:42] Your friend is right
[00:42:45] Let's see why
[00:43:18] Like I said before, when you consider the expression inside the absolute value is negative, you have to add a minus in front of it
[00:43:23] that would be like this:
[00:43:54] Can you spot where you got it wrong in your expression?

Guest (Customer)
[00:44:20] yes i understand now
[00:44:42] thank you!!!

Lucia F (Tutor)
[00:44:47] Excelent!

System Message
[00:44:48] *** Lost connection from Guest (Customer). Waiting for reconnect... ***


Math - Calculus occurred 4/26/2016 @ 5:49PM and lasted 44:46
Hi, I need help with these problems. [ File > http://lhh.tutor.com/SharedSessionFiles/6c98f7ec-4419-4df4-a6e7-afa0ba96a812_Screen_Shot_2016-04-26_at_5.22.07_PM.png ]

SYSTEM (System)
[00:00:00]*** Please note: All sessions are recorded for quality control. ***
Guest (Customer)
Lucia F (Tutor)
[00:00:12]Welcome! Let's get started.
[00:00:19]Give me a minute while I look at your problem :)
Guest (Customer)
[00:00:34]hi! okay no problem
Lucia F (Tutor)
[00:03:00]I'm working on this...
[00:03:08]Alright
[00:03:13]Do you know how to start this problem?
Guest (Customer)
[00:03:20]i started the first one but i am stuck
[00:03:38]i'll show you how far i got
Lucia F (Tutor)
[00:04:01]Okay!
[00:04:10]Oh sorry, added the image in the middle of your writing!
Guest (Customer)
[00:04:47]now i am not sure what to do
Lucia F (Tutor)
[00:05:25]What method did you use to try and find the interval of convergence? What does that formula account for?
Guest (Customer)
[00:05:41]i used the ratio test
[00:05:52]i am stuck i have no idea how to do this
[00:05:59]like how to find the interval of convergence
Lucia F (Tutor)
[00:06:09]Okay, let's work on it togheter
[00:06:40]So you have to find the interval of conevrgence and tried the radio test... Let me check the formula you got is right
Guest (Customer)
[00:06:45]ok
Lucia F (Tutor)
[00:08:11]Can I ask why you took the absolute value of x?
Guest (Customer)
[00:08:38]because the ratio test is the lim as n approaches infinity of the absolute value of an+1/an
Lucia F (Tutor)
[00:09:11]Oh, you're right :) I forgot that one detail of the absolute value in the ratio test
[00:09:23]Ok, so you got the limit in the ratio test is the absolute value of x
[00:09:38]and what does the ratio test tell you about convergence?
Guest (Customer)
[00:09:54]i don't know, i'm confused
Lucia F (Tutor)
[00:10:45]That's alright :) Do you know how to use the ratio test? When does it say the series converges?
Guest (Customer)
[00:11:00]no idea haha
Lucia F (Tutor)
[00:11:26]Alright, let's start from there!
[00:11:33]Like you said, the radio test is this...
[00:12:15]You know that definition, right?
Guest (Customer)
[00:12:28]yes
Lucia F (Tutor)
[00:12:41]When L < 1, the infinite sum for an convernges
[00:12:54]when L > 1, the infinite sum for a_n diverges
[00:12:56]correct?
Guest (Customer)
[00:13:06]yes
Lucia F (Tutor)
[00:13:34]And you got |x| for the series in your problem
[00:13:48]How can you use that to find out where is diverges and where it converges?
Guest (Customer)
[00:14:29]i don't know
Lucia F (Tutor)
[00:15:10]I'm sure you can do it :) Tell me again, when you use the ratio test, you know the series converges when you get what kind of number?
Guest (Customer)
[00:15:23]one that is less than 1
Lucia F (Tutor)
[00:15:42]Good! And for the series you want to test, what did you get?
Guest (Customer)
[00:15:49]x
Lucia F (Tutor)
[00:16:18]Great! so if you wanted the series to converge, what would x have to be?
[00:16:22]|x|*
Guest (Customer)
[00:16:32]less than 1?
Lucia F (Tutor)
[00:16:39]Excellent!
[00:17:06]Do you see now the condition you got for x? :)
Guest (Customer)
[00:17:11]yes
[00:17:16]so what is the interval?
Lucia F (Tutor)
[00:17:19]That's a first step towards the inteval of convergence
[00:17:38]well, if it has to be |x| < 1, what would x be between?
Guest (Customer)
[00:18:02]from -1 to 1
Lucia F (Tutor)
[00:18:07]Good job!
Guest (Customer)
[00:18:18]but how do we know whether each of those values is included or excluded
[00:18:28]like when we write it, if it has a parentheses or bracket
Lucia F (Tutor)
[00:19:04]What has to have parentheses or brackets? I don't understand, sorry
Guest (Customer)
[00:19:20]if it's (-1, 1] or (-1,1) or [-1,1] etc
Lucia F (Tutor)
[00:19:27]Oh!
[00:20:03]Well, you know from the ratio test that if L is exactly 1 then the test is not useful, right? L has to be exactly less than 1
[00:20:16]so if |x| has to be exactly less than one...
[00:20:34]what would that mean, say for positive x's?
Guest (Customer)
[00:20:58]they have to be less than 1?
Lucia F (Tutor)
[00:21:24]That's right, does that mean they can be 1? :)
Guest (Customer)
[00:21:36]no
Lucia F (Tutor)
[00:21:56]Great! So would you use parenthesis or brackets for 1 in the interval?
Guest (Customer)
[00:22:11]which one means what?
Lucia F (Tutor)
[00:22:38]Parenthesis means it's not part of the interval, bracket means it is
Guest (Customer)
[00:22:47]so then it will be parenthesis
Lucia F (Tutor)
[00:22:54]Great job! :)
Guest (Customer)
[00:23:07]so [-1, 1)?
Lucia F (Tutor)
[00:23:39]The -1 is the same. Do you know how to evaluate inequalities iwth absolute values?
[00:23:48]I can show you how
Guest (Customer)
[00:24:27]no
Lucia F (Tutor)
[00:24:59]Alright, let me show you quickly how to do them
[00:25:09]Let's do the same as this example
[00:25:30]You have to divide it in two.. One for positive x's ....
[00:25:56]Which means the absolute value remains the same, since it's already positive
[00:26:06]And one for negative values...
[00:26:38]When you remove the absolute value bars from a negative unknown number (any negative x) you add a minus sign in front of it :)
[00:26:51]That way, x becomes positive!
Guest (Customer)
[00:26:54]ok
Lucia F (Tutor)
[00:27:25]Now, how do you clear out the x in the negative one?
Guest (Customer)
[00:27:36]divide by negative 1
Lucia F (Tutor)
[00:27:56]Good! and what happens? You have to be careful with that step
Guest (Customer)
[00:28:04]inequality flips
Lucia F (Tutor)
[00:28:09]Excellent!!
[00:28:24]And you get this, is that right?
Guest (Customer)
[00:28:29]yes
Lucia F (Tutor)
[00:28:49]No it's not haahah I wrote the inequality sign wrong, sorry :)
Guest (Customer)
[00:29:01]oops haha
Lucia F (Tutor)
[00:29:11]Very well
[00:29:18]So what is the resulting interval from this?
Guest (Customer)
[00:29:26][-1,1]?
Lucia F (Tutor)
[00:29:47]That's almost right! Remember they are not included!
Guest (Customer)
[00:29:56](-1,1)?
Lucia F (Tutor)
[00:30:03]If they were included, the inequality sign would be this:
[00:30:11]Correct!
Guest (Customer)
[00:30:20]yay
Lucia F (Tutor)
[00:30:33]those I wrote on the board, with an extra line, mean less than or equal to, and greater than or equal two
Guest (Customer)
[00:30:38]yes
Lucia F (Tutor)
[00:30:39]they are different :)
[00:30:44]Great!
[00:30:59]Only when they can be equal to that you use brackets :)
[00:31:14]Alright then, want to try the next problem and see if you got the concepts right?
Guest (Customer)
[00:31:29]yes i actually tried it already and wanted to check it with you
Lucia F (Tutor)
[00:31:42]Good! Let's see then :)
Guest (Customer)
[00:32:12]i'm going to show you the final steps because the earlier ones are all just rearrangement
Lucia F (Tutor)
[00:32:39]Okay!
Guest (Customer)
[00:33:44]tell me if that's right
Lucia F (Tutor)
[00:34:22]The answer you got is correct! But remember to not omit terms when writing the limits since teacher don't normally like that in exams :)
Guest (Customer)
[00:34:37]like which terms?
Lucia F (Tutor)
[00:34:59]Here, you didn't keep writing the |x|
Guest (Customer)
[00:35:03]right
Lucia F (Tutor)
[00:35:17]Even though it's right the limit of the following part is 1
[00:35:24]But What you get is |x| as the result
[00:35:32]and that is what has to be less than one
[00:35:51]It's a common thing students don't think they have to write and teachers don't like it :)
[00:36:16]Alright, so did you understand everything we did to get the interval of convergence?
[00:36:32]Can you write down the final result for that one as an interval too?
Guest (Customer)
[00:37:46](-1,1)?
Lucia F (Tutor)
[00:37:52]Great!!
[00:37:58]You did really well! :)
Guest (Customer)
[00:38:11]thank you :)
Lucia F (Tutor)
[00:38:35]Was everything we did clear to you? Do you need help with anything else?
Guest (Customer)
[00:40:32]yes i need help with one more thing that i am stuck with relating to this
[00:40:46]it's a different problem but i am having trouble with the final inequality that i got
Lucia F (Tutor)
[00:41:06]Okay, let's see it!
Guest (Customer)
[00:42:09]is that right??
[00:42:24]because one of my friends got (-1,5) instead of (-5, 5)
Lucia F (Tutor)
[00:42:31]The one on the left yes, it's right
[00:42:42]Your friend is right :)
[00:42:45]Let's see why
[00:43:18]Like I said before, when you consider the expression inside the absolute value is negative, you have to add a minus in front of it
[00:43:23]that would be like this:
[00:43:54]Can you spot where you got it wrong in your expression?
Guest (Customer)
[00:44:20]yes :) i understand now
[00:44:42]thank you!!!
Lucia F (Tutor)
[00:44:47]Excelent!
SYSTEM (System)
[00:44:48]*** Lost connection from Guest (Customer). Waiting for reconnect... ***