# I have my Calc II final in 30 minutes

1. Dec 13, 2011

### QuarkCharmer

I needed to take a break from studying, and nobody was in PF chat to listen to my complaining! I need at least a 65 to keep an A. I don't know why I am so worried about it. Granted, I am out of practice on some of the earlier topics. Anyway, this course is sort of a milestone for me, because a little over a year ago I knew basically 0 mathematics, and I was told that Calculus II was probably the most difficult of the typical selection of courses (calc/deq). At least in (hopefully) passing this course with an A, I will assure myself that I am at the very least capable of higher mathematics. What's the next course that shares a similar "milestone" status? I'm told Analysis.

Anyway, wish me luck, and sorry for creating a pointless rant thread.

2. Dec 13, 2011

### Greg Bernhardt

Good Luck!!!!

3. Dec 13, 2011

### micromass

Staff Emeritus
Good luck quark!!

I'm sure you will end up with a great score! You might have to prove yourself to you, but I already think that you're great at mathematics!!

Keep us posted on how you did!!

Other milestone coures should probably be abstract algebra and real analysis. Not hard once you know it, but it can be brutal for newbies.

4. Dec 13, 2011

### Staff: Mentor

Have a great test!

5. Dec 13, 2011

Good luck!

Don't forget the arbitrary constant on those indefinite integrals! They get me every time. :grumpy:

6. Dec 13, 2011

### micromass

Staff Emeritus
http://memegenerator.net/cache/instances/400x/11/11970/12258100.jpg [Broken]

Last edited by a moderator: May 5, 2017
7. Dec 13, 2011

### lisab

Staff Emeritus
Oh micro....you crack me up!

Best of luck, QC, it's almost over!

8. Dec 13, 2011

### Staff: Mentor

:rofl:

Killing me here. Too funny.

Hey OP, how did the test go?!

9. Dec 13, 2011

### QuarkCharmer

Well, I took it alright. There were two problems that I think I messed up something on, but overall, I think I probably scored around a 90. He's good about posting grades the next day if not the same night, so I'll know real soon.

The one that I just couldn't figure out asked me to list the first 4 terms in a Maclaurin Series representation of a function, and then use the Series as a whole to estimate an definite integral.

I believe it was:
$$\int_{0}^{\frac{1}{2}}cos(x^{2})dx$$

So, I recalled that:
$$\sum_{n=0}^{\infty}\frac{(-1)^{n}x^{2n}}{(2n)!} = cos(x)$$
and so, the representation was:
$$\sum_{n=0}^{\infty}\frac{(-1)^{n}x^{4n}}{(2n)!} = cos(x)$$
I used that Series, to list out the first 4 terms (for n:0,1,2,3).

I then put that series in place of the above integral, and the result was some series with 4n+1 and (2n!) in the denominator, that I couldn't quite manipulate to make it look like a known series. I was thinking it would come out to be geometric, well, sort of, it was alternating, so I tried using the alternating series test, but I couldn't figure out how to estimate it's value considering there was no error given to me. I know that:
$$|e| = |S-S_{n}| <= b_{n+1}$$
but again, no given error?

After that, they wanted me to find the 8th derivative of cos(x^2) evaluated at zero. There were 2 homework problems we did along time ago like this, but it wasn't coming back to me, this whole problem was a nightmare. I tried setting my series for cos(x^2) equal to the definition of the maclaurin series:

$$\sum_{n=0}^{\infty}\frac{(-1)^{n}x^{4n}}{(2n)!} = \sum_{n=0}^{\infty}\frac{f^{(8)}(0)x^{8}}{8!}$$

and then I set 4n = 8, to find the n for the left side (n=2). I put all n's on the left to 2, and did the math to solve for f^(8)(0) but I got some insane number in the hundreds that just did not seem right. So who knows...

Only my physics final to go!!

Last edited: Dec 13, 2011
10. Dec 13, 2011

### Office_Shredder

Staff Emeritus
11. Dec 14, 2011

### QuarkCharmer

12. Dec 14, 2011

### KingNothing

IMO, differential equations and quantum physics are the next "milestones", but it depends on your career path.

13. Dec 14, 2011

### QuarkCharmer

Update:

!!:!!)

14. Dec 14, 2011

### Staff: Mentor

Congratulations! Well done.

Next time - do better.

15. Dec 14, 2011

### micromass

Staff Emeritus
Niiiiiiiice

You have defeated Calculus II, but a new opponent awaits :tongue2:

16. Dec 14, 2011

I seem to remember a previous post by you (around mid-terms) where you were scoring higher on your assignments. I know it's the end of the semester, but that's no excuse for slacking-off, mmkay?

17. Dec 14, 2011

### QuarkCharmer

Oh yeah, that test I got a 115 on. I went into PF chat and asked micromass to look it over, because I thought it was really difficult considering the time they gave. Turns out, most people didn't finish it, and I just barely finished it. Due to the professors shortsight on timing, it was curved up 15 points.

I have no idea where the ~7 points came from on this one. I think it's from various one point extra credit things throughout the semester.

18. Dec 14, 2011

### Staff: Mentor

Yeah, better than the 107%. Slacker!

19. Dec 14, 2011

### micromass

Staff Emeritus
OK, now that you passed Calc II, we have to tell you something. It is something that is only known to people that passed Calc II. It is a secret but important knowledge. You are expected to keep this a secret for people not passing Calc II.

Here it is:

Last edited by a moderator: Sep 25, 2014
20. Dec 14, 2011

### QuarkCharmer

http://achtungtshirt.files.wordpress.com/2009/07/danger-sign-rickroll-rick-astley-funny-black-tee-shirt.jpg?w=450 [Broken]

Last edited by a moderator: May 5, 2017