Calculus 2 Final Review || Techniques of Integration, Sequences & Series, Parametric, Polar & More!
ฝัง
- เผยแพร่เมื่อ 28 ก.ย. 2024
- In this video we will be reviewing everything we have learned in Calculus 2. This video will consist of 30 questions which cover most of the Calculus 2 topics.
I will have a longer video available soon that will consist of 100 questions. I will update the description once I have that video made.
UNSURE ON ANY OF THE PROBLEMS WE DID IN THIS VIDEO?
Here is a list of all of my Calculus 2 playlists which are sure to help.
Prerequisite Review: bit.ly/2P1TA15
Applications of Integration: bit.ly/2NbihI0
Techniques of Integration: bit.ly/2MK820o
More Applications of Integration: bit.ly/2PxW34A
Parametric & Polar: bit.ly/2w87zLU
Sequences & Series: bit.ly/2Mrobsa
I hope this video helped! If it did, be sure to SUBSCRIBE for more content. Thanks for watching!
If my videos are helping you, consider supporting me on Patreon!
/ ludus1
#final #review #finalreview #calculus2 #calculus #calculus2finalreview
This video is really helping me get ready for my calc 2 final this coming Wednesday. Thanks for making this. keep up the dedication, the subscribers will come it's only a matter of time. Will share this with my classmates to show some support!
JAGR-9 I’m glad I was able to help! If you have any questions let me know. I’m considering making more videos like this for Calc 1, Calc 3, Linear Algebra, and Differential Equations.
I appreciate the positivity. I know the lower subscriber count is something that I’ve been worried about because I want to help as many people as possible, and maybe even do this as my job. But honestly, I’m just grateful for all of the support that you all have been giving me thus far. It’s already kind of crazy how many people I’m able to help, and I think that’s what keeps me going.
I really do appreciate you spreading the word!
Again, let me know if you have any questions. I’d be happy to answer any question that you’re struggling with.
Good luck on your final!
Josh.
@@LudusYT That would be awesome if you did! Maybe even calculus based physics too ? ? Me and my classmates would definitely tune in!
Are you an engineering major? Just curious because I have to take those exact classes plus a couple physics courses also.
Thanks man I really appreciate it!
JAGR-9 I’m a physics major actually, so I would also be doing those finals as well lol.
Btw sorry for the late response. It doesn’t give me notifications when someone actually responds to my comment.
Ironically the same here my finals next week Wednesday.
Hi, I just wanted to drop you a note of appreciation. I failed calculus 2 twice (badly) some fifteen years ago when I first went to university fresh out of high school. I ended up dropping out of my program. Well I'm back to school after all this time, and I just got my final mark back for Calc 2, and I passed it with a 96%!! And your videos are a big part of the reason why.
4 years later after uploading, this man still helps me. You explained all the problems in great detail. My exam is tomorrow, thank you legend!
got my final in 7 hours, im feeling a lot better after watching this thank you
1) 1:19 Area Bounded by Curves
2) 8:26 Volu. by Revolv. the Region
3) 12:23 Shell Method
4) 20:33 Average Value
5) 24:50 Integration by Parts
6) 30:47 Trig. Integral
7) 34:54 U Substitution
8) 37:13 Inverse Trig. Sub.
9) 45:29 Partial Frac. Decomp.
10) 56:51 Comparison Test
11) 1:00:06 Arc Length
12) 1:04:40 Surf. A. by Rotating y=
13) 1:09:32 Parametric Equations
14) 1:12:58 2nd Deriv. of Para. Equa.
15) 1:16:31 Arc.L of Param. Equa.
16) 1:18:57 Grahing Polar Equa.
17) 1:23:14 Slope of Tang. Line Polar
18) 1:25:42 Area of Polar Equa.
19) 1:28:17 Sequences
20) 1:32:46 Series
21) 1: 34:22 Divergence Test
22) 1:36:32 Integral Test
23) 1:41:34 Comparison Test
24) 1:44:40 Limit Comparison
25) 1:48:11 Alternating Series
26)
27)
28)
29) 2:06:15 Maclaurin Series
30)
goat
26. 1:56:41 ratio test
27. 2:00:00 root test
28. 2:03:00 comparison test
30. 2:09:23 Taylor series
1:34:22
my test is in 2.5 hours perfect time to find this
me rn
3h for me rn wish me luck boys
@@jgr00t69what happened?
@@wibleston got a 78 lol
This is great review for the final. I have re-watched this a couple times this semester. I really appreciate you putting time into this. I hope you continuously get the support from your fans because you deserve it!!!
Andre Abtahi - I’m happy I could help, and I appreciate the kind words. We actually just hit 500 subscribers yesterday, so hopefully 1k is right around the corner!
In any case, I really appreciate your support. It means a lot and it really keeps me going.
Btw, I’m currently working on a Special Relativity series which I may be able to start posting by early June. You’ll definitely want to check it out because the quality will be MUCH better than that of this video. Maybe that will be my big break!
im only 30 minutes in the video and I have found this channel the most helpful for calc 2, not chemistry tutor guy, not black pen red pen, not professor leonard but only you. Thanks so much!
at 21:45 the derivative of cos(x) is -sin(x). You forgot the negation symbol
correct me if im wrong but you forgot the negative at 27:29 when plugging in v du where du is -sinx which wouldve made the integral positve
yea, i noticed it too
I see what happened, theres no parenthesis but you have to distribute a negative and that would make the intergral negative
Am grateful for the best examples given.
Amazing summarization of a large subject, thank you!
1:36:00 DICLARR
Really well explained, thank you so much!
Chen Studios - I’m glad I could help! Good luck on your final!
yooo this dude is a smart guy like he explains things very well but these different methods are not what i learned in college so i’m getting lost on a few of them😭😭😭
At 1:16:28, why can you not do quotient rule on dy/dx to get d^2y/dx^2?
I just finished my Calc 2 course and I ended up with a 93.16%. Should I be very proud of myself?
yes that’s great congratulations🎉, wish me luck my final is in few days and i need to pass😢
@@xxcovsi1226 I actually got a 93.16%, but I wish you the best of luck. You can do this!
Hey on problem 9, when you did the U sub we changed the bounds, you then evaluated the integral at the former bounds (0 to 1) instead of (1 to 2) just wondering if you purposely did this or it was just a mix up. Thanks! Video is super helpful.
He also forgot to plug the U sub back into the equation after he integrated U. It should’ve been 1/(x+1) from 1 to 2. Nvm I wasn’t properly taught, had to figure out on my own that when you change back to X you use the original bounds. You only use the U bounds if you keep your integral in terms of U
Thanks for your hard work! It was awesome.
Thank you for the help, I have a final on Monday and I have a very hard time motivating myself to practice problems, but this video is perfect for what I need! I def had to subscribe, and some calc 3 videos would be appreciated in the future (taking it next semester) !
Noah Rosenstein Not a problem! I’m glad I could help! I actually have my last final Monday lol (Physics 3).
I know exactly what you mean about the motivational issue. I got that when studying for my linear algebra final I had today (on a Saturday...).
I think the biggest problem is that you have to find what problems to go over, and that’s kind of the big barrier to entry. With this video, I’ve already done that for you, so I figured I could help students get around that.
I’ll be making videos on the hardest topics in calc 3. They’ll be longer videos that cover everything rather than the shorter videos that I’ve been doing.
This is just because my longer videos will actually rank in search, so people will be able to see them (I’m still a fairly small channel).
I really appreciate the support!
@@LudusYT it sucks that they have exams on weekends my university is like that too luckily i have only had midterm exams on the weekends no finals...thank you again and good luck on your physics final!
Noah Rosenstein lol I just got unlucky this semester, no biggie ig. Thanks again, good luck on your calc 2 final!
Super video! I applauded for $10.00 👏👏👏
Why is the radius in question (2) 1/x?
Great help, thanks very much
No problem homie!
Great video my guy
Samuel Chilson - Thank you!! I’m glad I could help. Let me know if you have any questions.
Thank you so much!
Discount Legolas - No prob! About to finish up part 2 of calc 3 final review video so you’ll have that for this May if you need it!
Amazing video!
thank you
At 17:40 , why is the distance x and not x^2 ? Because I thought since y = x^2 for that line, the distance from the y-axis would be x^2 . Or maybe I'm dumb idk, im literally retaking calc 2 right now and have my final saturday lol
Great question. If it was 4-y then we could be plug in that y=x². However, we’re dealing with a horizontal distance here, and a horizontal distance from the y-axis is what we call x. Does that make sense?
@@LudusYT ohh okay I get it, thank you!
@@allysplaylists glad I could help!
1:34:09
Mistake? Shouldn't we say, by divergence test, that because lim n->inf of a_n =/= 0 this series diverges
Thomas Balcom Good question. This isn’t a mistake, because a_n and s_n are two different things. You do the divergence test with a_n not the nth partial sum (known as s_n).
When you take the limit as n approaches infinity of the nth partial sum, you are actually finding the sum of the series.
@@LudusYT Ah, thanks, understood
Thomas Balcom Not a problem!
Thanks alot
wait for the cos^4xsinx how did he just do the u sub with out trig identities
the derivative of cosx is -sinx so he can just cancel out the sin and have u^4 with a negative outside
you saved me man
on 27:39 isn't it suppose to be positive integration of e^x sinx dx
Akeem Louigarde Great question! I see how this could have confused people. I should have shown an extra step.
After we did our first integration by parts, we had that negative integral of e^x cosx dx.
That negative gets distributed when we do our next integration by parts.
So it makes e^x cosx negative, and it makes integral of e^x sinx dx negative.
I hope this helps!
You are a legend
Thanks
Looks like a great video but you can't read it it's to small.
Haven’t heard of that problem before? Try using a bigger screen.
You should make a paypal for donations because I feel like most people don’t want to commit to a subscription service
Ur thinking like Venmo?
Btw it’s not a subscription service. Plenty of people drop one time payments.
Ludus www.paypal.me Venmo works too I guess but imo PayPal is more precessional
*professional
Ludus yes .but u have to remember to cancel at the end of the month. I just meant to also include another form to support your work that’s 1 time and no frills
this guy looks like orangepeanut.. great video tho, thank you!
I HATE CALC
BOO HOO I love calc!
I am an engineering student who is about to take his first Calc 2 class and I have been surfing the web reviewing Calc 1 and now preparing myself for Calc 2 and I just want to say the way you explain things in such a clear and concise manner has earned my respect and subscription. From one college student to another I will definitely support on Patreon once this financial aid reimbursement comes around hahaha good work man, definitely make videos for Calc 3 and so on!
Kingsley Andrews - Wow, thanks so much man! I’m glad I could help out. It’s kind of funny because I created those calc 2 videos while I was taking calc 3. My class actually had a pretty good teacher, but the average test score was still in the 40’s-50’s, so I knew I had to do something. I proceeded to create these videos where my primary goal was just to be as relatable as possible. I knew exactly where the hardest points were for calculus 2 students, and so I made sure to break down/explain as thoroughly as possible.
I will be working on more Calculus 3 videos towards the end of this semester. I am currently working on my Special Relativity series on YT, and after I complete that I’m going to work on wrapping a full, higher quality calculus 2 course which I will have available on my website. I’m also going to make a few longer calculus 2 videos with the higher quality setup and post them on YT. I’ll follow a similar strategy for the calculus 3 course that I will make directly after I finish that one. Hopefully it will be out by the start of the spring semester! I keep everyone up to date on Patreon where I post my daily progress.
If you’d like to talk more, feel free to DM me on ig at learned_tutoring.
What classes are the toughest as you move up and what engineering major are you?
I have my final exam coming up and this video helped me out tremendously. Thank you!
Hey man! This video was super helpful! I have my calc 2 exam tomorrow and I was looking for a review of everything. This not only helped me review everything. but taught me some things that I had forgotten or never really fully understood in the first place. Thank you for putting so much time and effort into this video so others can succeed.
1:34:20 WOULDNT THIS DIVERGE DUE TO NTH TERM TEST?
yes, harmonic series
Had a really bad life event happen In the middle of a Calc 3 semester that forced me to drop it years ago. Using your videos to brush up and it feels just like riding a bike...thank you so much
You look like Thom Yorke
This guy shows that not all heroes wear capes, but blue polos
Great stuff I'm using it for my final that I have tomorrow. Do you by any chance have some sort of a Calc 2 "cheat sheet" which is like important ideas + formulas summarized in a few pages?
Abublaa - I’m glad I can help! I don’t have a cheat sheet, but I think that is a really great idea for a video and I will definitely make that in the future. That won’t be in time to help you for your final tomorrow so I’ll try my best to give you some ideas of what I would right down.
I would definitely make sure to write the four cases of partial fractions, some other integral formulas like inverse trig and integration by parts, and then possibly some polar formulas (especially if you hate polar lol). Also be sure to include the different series tests including absolute and conditional convergence. Include the formulas for Taylor and Maclaurin series, and also write down any common Maclaurin series such as e^x or sin(x).
I hope this helps! Thanks for all your support, and I hope you continue to find my channel useful in the future.
I was looking all over for this type of video! This will certainly be put to good use before I take calc 2 in the spring. Thanks for the hard work you put into these videos :)
WreckingWall I’m glad I could help!!
I really wish more people could see this video, but it doesn’t really rank in search at the moments, so no one sees it.
It’s the perks of only having 100 subs lol 😂
I wish teachers taught like this cuz it would make it so easy to do well in class. So many of my teachers seem to forget they’re teaching like they will either skip steps completely or just do everything in their head and then ask us if it checks out. Like I don’t know, you haven’t taught anything yet, you just solved a problem on the board and expected everyone to know what you’re doing. The entire point of teaching is walking through the entire problem and showing people what to do and how to recognize mistakes.
For partial fractions, which starts at about 45:30 in the video, you guys can look up the "cover-up method" to find the constants A, B and C instead. Great job so far in the video. Very in depth review of calc 2 topics.
Deadly3nemy - I’m glad I could help!! I’ve never heard of a “cover-up method” but I’ll have to take a look sometime.
We actually used the technique I’m using in both calculus 2 as well as diffy q (which I just finished up). I have my own videos that dive deeper into this partial fractions method, but it’s interesting to hear that there are other methods out there.
@@LudusYT your way of doing it is perfect when you get quadratics as denominators for partial fractions. The cover up method only works when the denominators are linear factors. When they are linear factors cover-up method is the way to go. The link for it is here: www.google.com/url?sa=t&source=web&rct=j&url=math.mit.edu/~jorloff/suppnotes/suppnotes03/h.pdf&ved=2ahUKEwjAmfveyZniAhUMeKwKHU_EBrsQFjAOegQIARAB&usg=AOvVaw2rVQTu0AVGbpVC7kAdSjKq&cshid=1557789594189
Also the PDF doesn't clearly state that to find the x value, you set the denom of the separate partial fractions equal to 0.
Deadly3nemy - Awesome, I’ll definitely look into it. Thanks!
not sure if this is sad to admit, but im a 5th year undergrad obtaining a BS in applied math. and to graduate (at my school particularly) we take something called a computational exam, which analyzes how well you understand your major. out of 6 exams this month, our calc exam is first and I havent done this material in 3+ years and let me say, as someone with [almost] a math degree, this is about as clear and concise as it gets. absolutely wonderful work and you have helped me so much remember everything I thought i forgot. thank you!
Well done Josh, be patient, you'll have a ton of viewers & subscribers with time :) Looking forward to more videos.
If I may: My calc II exams had MUCH harder questions on them. If you can get your hands on Briggs / Cochran Calculus Early Transcendentals (2nd ed) - problem sets at the end of each chapter. We were asked the more difficult questions.
Xopher Thanks for the kind words! In that 8 hour video that I will be making in the next month or so, I will be going through much harder examples.
My whole idea with this video was just to try to cover every single topic in the shortest amount of time. Then, if there was anything that you didn’t feel comfortable with, I have videos in my calc 2 playlists that explain the topic in further depth and go through harder problems as well.
I hope it still helped you out though!
Josh.
DICLARR, definitely gonna use that! You best be makings tons of review videos; it's that time of year!!!
Lucas McMasteur - I’m glad I could help! Yea I wanted to make way more final review videos but I got caught up with my own classes a bit. I have one now for calc 1, calc 3, linear algebra, and college algebra, and they are much higher quality than this one (new setup).
Let me know if you have any questions!
i subscribe, this helping me so much so far for my calc 2 midterm tomorrow (especially after feeling burnt out, lacking motivation and being frustrated over not understanding any of the content), I'm starting to gain hope that I an at least pass this midterm (will definitely be back for the final)
this dude look like lip from shameless
where can i find the link for the 100 question review?
its December 14 2021 getting ready for my finals and this vids has a lot of info. shout outs to you
Love that you have this type of video, I’ll be sure to refer back to some it when I take calc 2 at college next fall. Just saw this channel so idk if there already is, but I hope to see something like this for calc 3 and maybe some differential equations/linear algebra in the future
Alex Boughlef - I’m glad that I can help! I am actually working on mass producing these final reviews right now so it’s funny that you say that. I assume that you are in Calculus 1 at the moment if you are taking Calc 2 in the fall. I just released the calculus 1 final review videos a couple days ago. You can check my vid feed for those if you want!
I also have just released Calculus 3, and am currently working on Linear Algebra. I will be doing ODE in the future, but I’m actually taking that class right now so I will probably make it as a way to study for my own final.
I am probably going to remake this video because my new setup is much higher quality, and I feel as though I could have made some of these problems slightly more challenging. Let me know if there are any other videos that you want to see made!
Josh Martin glad to hear it. Saw that you’ll be doing physics videos too which will be just as helpful. I Appreciate the vids!
Alex Boughlef - No prob! Let me know if you have any questions! You found this channel early so you get to watch it grow. Hopefully soon I’ll be at 1k subs. We’ll see lol.
where are the 100 question vid did you make it?
software engineer here who is just doing this for fun lol you make it so easy to remember its actually just enjoyable
Wouldn't question 26, at 1:59:25, you would leave the (n+1)^4/n^4 as they are, then solve the next two parenthesis and eventually the equation in the next step would become \lim_{n \to \infty} \frac{(n+1)^3}{n^4} which the limit would go to 4 instead of 0?
thank you chef
Using this video to help study for my final on Friday. Thank you for the video!
Musical Comedy - Not a problem. I really hope it helps!
lip gallagher ???
Man this is awesome, thank you so much! You better be getting lots of money from ads on this video, it's worth it! XD
this guy makes me enjoy calc 2 meanwhile my professor makes me dread it :(
Perfect review questions, really helped man thnx.
Mason Schwalm I’m glad I could help!
This randomly came on my feed Becaude TH-cam. I went up to precalc in highschool and stopped doing math for years……….what am I looking at..? It’s actually scary ngl……
For #10 at the 1 hour mark can you say the function is convergent by p-integral since p=2>1 or does the p-integral only work within certain bounds/intervals?
David - That’s a great question. I think you are getting a little mixed up with series. When proving if a series is convergent or divergent, you can use the p-series test, but I don’t believe you can label something a “p-integral”.
I only say this because it wasn’t something we learned in my calculus 2 class, but maybe it was something that you learned in yours. If it was then definitely roll with it.
Let me know if that makes sense, and if you have any other questions!
Josh.
@@LudusYT Here are some examples of this test for improper integrals:
th-cam.com/video/TKIdC847K3k/w-d-xo.html
th-cam.com/video/rwLkrGrugOk/w-d-xo.html
I believe it works the same way for both improper integrals and series if you just want to find out whether the function converges or diverges without evaluating it. Your videos are great by the way!
David - I’ll definitely have to check it out! Like I said, it makes perfect sense to label something as a “p-integral” because of the similarities between improper integrals and series, but it wasn’t something that I was taught in my calculus 2 course so I didn’t want to tell you the wrong thing.
I appreciate you taking the time to show me those links, and I’m really glad my videos have helped you!
Thank you so much going through all of your calc 1 2 and 3 reviews in prep for my Vector and Complex Analysis class after have not taken any calc for like a year, this is so helpful! I watched your videos back when I was in those classes too
good video but just skips to many small steps when solving the problem which makes it more confusing
thank you for allowing me to affirm for myself that i am totally fucked on this final lmao
I have a final on thursday and this video is gonna help me a ton! Thank you
Galaxy Fennec - No problem! Let me know if you have any questions.
My finals are actually next Saturday and Monday so I’ll wish you luck if you wish me luck lolol.
Galaxy Fennec - No problem! Let me know if you have any questions.
My finals are actually next Saturday and Monday so I’ll wish you luck if you wish me luck lolol.
@@LudusYT Goodluck on your finals! Thank you for all these tutorial videos
😭😭 this is gonna be a tough night for me
didnt know lip from shameless moved from netflix to youtube
at 28:00 the derivative of cos(x) is -sin(x), so wouldnt work
does some one know what formulas would be good to study and memorize.
Hey Josh, I saw a small error at 27:30 when you were writing the integral of e^x*sin(x) when it should be - sinx since du is -sin(x).
unless I was seeing it from a wrong perspective.
Huh, so I either planned to do that, or I made two consecutive mistakes that allowed me to still get the problem right lol.
Regardless, you have to remember that when we do that second integration by parts. That integral that we perform ibp on has a negative on it, and so we need to distribute it through when we do the ibp. If you distribute the negative through (giving the integral a + sign) and account for the -sin(x)dx as you pointed out, the integral now has a negative sign.
I feel like I did that on purpose, but I obviously should have explained that more. That's a complete failure on my part. Thank you for pointing this out!
18 year old me needs a lesson on how to explain things.
But hey, your still the freakin bomb man. Best virtual tutor I ever had. Thank you.
27:29 You say 'negative' sinx dx * e^x but wrote positive e^x sinx?
how is 20 convergent but 21 is divergent
I wish I discovered this channel earlier
1:31:33 why plug 1 not 0
?
For Question 10, you can technically factor x^3+1 as (x+1)(x^2-x+1) and then use partial fraction decomposition.
just finished calc 1 and watching this for fun 😅explanation is really good but think i need to start from the beginning now 😂
Even though this video didn't cover everything which tbf is pretty unreasonable, Combined with cramming the Organic Chemistry Tutor's video with this one the day before the exam I got a 96% For those wanting to do well make sure to go remember all the arc length formulas (It wasn't in this video so I forgot it and got points taken off for it).
I’m glad you did well on your exam and I agree. It’s unfortunately unreasonable to expect me to be able to cover everything your specific course covers. This is basically everything that my course covered at my university, so I’m glad most it overlapped with yours! The arc length formulas I showed in this video was probably everything we learned, but I’ll have to look back and see if there anything I can add. I want to remake this video this summer.
19:38 isn’t it 8x squared?
i would be so fried tomorrow if not for you
I have a question on the series test: why would you choose integral test in Q22 ? Because for me,comparsion test is much easier. Is integral test have any advantage(my professor also prefer using it,I'm curious about that) that you decided to choose it?
Good question! There was never a point where I actually compared two tests and said “I think this one will be easier”. You may be absolutely correct - a comparison test may be easier. I didn’t want students to have to worry about doing that extra mental labor if they already feel uncomfortable enough with the tests (most are just trying to cram this video before finals).
So what I did in this video is introduce an acronym “DICLARR” which comprises all the series tests. I then go through the tests one by one until I find one that works. It just happens to be that the integral test comes before comparison. It’s certainly not that I think integral is easier though maybe that argument can be made. Hope this helps!
@@LudusYT Thanks for further explanation.❤️
Professor Ludas, thank you for an outstanding explanation and analysis of Calculus Two Final Review. The problem set is excellent, however in problems 7,8,9 and 30 equal signs are missing between the problem and the final solution. Equal signs are very important in all levels of Mathematics. Please correct these errors in the video.
i love you man
Sadly, this did not help with my calc 2 final, as my prof. decided to make our final a bit more challenging than any of the example questions that were shown here. But this video did help me understand some concepts a bit better and I will definitely be learning more from the internet/TH-cam than relying on my professors, as I have learned that their teaching methods do not suit my learning style.
Retry 44:11
It would be great if the audio is louder
My Goat
from Morocco i just find and discover your chanel...i m an old man Math lover to death...i love Math....and i want to thank you for those videos and tutorials
what is the difference between 20 and 21. Why wouldn't 20 diverge because the limit did not equal 0
THANK YOU SO MUCH Studying for my final on thursday and this vid is a god send
Awesome review. Thank you so much!
Glad you liked it!!
Hey man just stoping by before my mid-term and I wanted to say thank you very much. It's stupidly helpful even 4 years later, thanks!
I just had one minor doubt. At 1:31:47 why is the bound 1/7 and not 1/5. You chose n=1 to be the first term in the sequence but why can't we consider n=0 as the first term.
Geet Purohit Great Question! I’ve always been taught to start sequences at n=1, so that is simply what I did here. In this example, you’re right in that it absolutely makes sense to use n=0 as the starting term. However, when I was in calc 2, we never used n=0 or n= (anything negative).
Do you start sequences at n=0?
Josh Martin you're right I haven't really seen n=0, but when we do Taylor Series we always start with 0. I guess it depends on whether n is an integer or a whole number. Is 0 an integer?
Geet Purohit 0 is both a whole number and an integer. As you said, the only time you should see n=0 is when doing some kind of power series, whether it’s the Taylor Series, Maclaurin Series, even just differentiating power series and moving that index around (the n=whatever is referred to as the index).
I hope this helps!
Josh Martin thank you so much! I'll spread word on how great your videos are and don't stop uploading because one day you'll grow very big
Geet Purohit I appreciate that! I’ll work on more final reviews over winter break.