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  1. R

    Vector arc length problem

    Thank you. I'm sorry for the nonsensical post, I guess I was way too tired to not have that jump out at me. Again, thank you.
  2. R

    Vector arc length problem

    Homework Statement Find Arc Length: r(t)=t^3 i+tj+(1/2)\sqrt{6}t^2k 1\leqt\leq3 Homework Equations The arc length formula: integrate: sqrt((dx/dt)^2+(dy/dt)^2+(dz/dt)^2) dt The Attempt at a Solution I can find the derivative and plug into the formula, it's just the simplification that is...
  3. R

    Differentiating a function

    think of (1/3)*sin^3(x) as (1/3)*(sin x)^3 then apply the chain rule :)
  4. R

    HS students: what's a 'C' on your grade scale?

    I'm in South Carolina with the Uniform Grading Scale, and that is what we use. GPA is a different animal though, what with APs and IBs and all... I'm not even 100% sure how the GPA's are calculated anymore. I just do what I can and hope for the best.
  5. R

    Schools Compare universities

    It does get up to 100 or slightly higher, but it's not too common. Maybe 3 or 4 days a year. It's times like that we're thankful for air conditioning! As I said before, I have not a clue as to the graduate schooling, maybe someone else can aid here.
  6. R

    Schools Compare universities

    Cost of living in South Carolina is quite low in general compared to a majority of the United States. I can't quote numbers, you'd have to do some research yourself for that. The college itself has it's system of buses and whatnot, but you are within walking distance of really almost all of...
  7. R

    Schools Compare universities

    I live about an hour away from Columbia. I have to say, I do enjoy the atmosphere of South Carolina. The University itself can get VERY hot during the summer, and it's quite humid down here as well so the heat is quite intense (especially since the college is IN the city). BUT starting in...
  8. R

    How do I perform these functions without using a calculator?

    http://www.itl.nist.gov/div897/sqg/dads/HTML/squareRoot.html That's a method of computing square roots by hand. http://www.itl.nist.gov/div897/sqg/dads/HTML/cubeRoot.html That's a method of computing cube roots by hand. http://www.uconn.edu/~cdavid/latex2html/mathreview/node18.html [Broken]...
  9. R

    Test Taking

    Testing is all about mentality. You've got to walk into that room like you own the place, bordering on arrogance that you know the material so well (even if you don't!). Convincing yourself that you can and will handle this test with relative ease is the ticket! All of this along with having...
  10. R

    Infinite series

    most definitely. notice how all terms have the same exponent...
  11. R

    Give the Limit

    Ah, yes I was wondering if that was your question. Well the proof exists online... it's not too terribly difficult. To prove that (where x is some constant) \mathop{\lim }\limits_{n \to \infty } (1+\frac{x}{n})^{n} = e^x We first set the limit equal to an arbitrary variable (y for instance)...
  12. R

    Give the Limit

    All they've done is given x a value. And since the two expressions are equivalent, when x is a specific value in one expression, to remain equivalent x has the same value in the other. So all your teacher did was substitute -1 for x?
  13. R

    Series either converges or diverges

    Have you learned of the Ratio Test yet? It would simplify this problem greatly. Otherwise, just to show that \frac{1}{n^{n}} diverges, that can be re-written as n^{-n} which would not equate to zero using the nth term test for divergence, therefore it DOES diverge. I haven't looked at your...
  14. R

    Senior year HS schedule

    That's a good way to put it. I didn't mean it was a cake walk, simply that it was about as easy as any other more advanced level math class. And personally we do a lesson a day (besides 4 or 5 of the more complex topics) and I find it demands the attention which is needed to succeed. So...
  15. R

    Senior year HS schedule

    At our school it is typical to take Precalculus (introduced to the basic limit and derivative at the very end of the year) our junior year, and then go to AB or BC depending on your grade in the class. Or you could be like me and slack off wayyy to much then go around the system to get in and...
  16. R

    How do I show sin 1 + sin 2 + sin 3 + diverges?

    I would just do what's already been mentioned and write the series as \sum_{n=1}^{\infty}sin(n) then just perform the nth test for divergence to show that the limit as n approaches infinity of sin(n) is infinity, and therefore NOT zero, and therefore it DIVERGES. And as otherwise mentioned...
  17. R

    Integral of product

    As a calculus student myself, the method we use is slightly different (and I think more commonly taught). Instead of keeping the 1/2 in the integral, since it is a constant, pull it out to the front of the entire integral, complete the integral, then multiply it by the 1/2 again. So \int...
  18. R

    Another convergent and divergent

    Ah good catch! I was not paying close enough attention, I apologize. But I did prove divergence by the Integral test... so I get some slack right? :) No but in all seriousness I do apologize, for lack of a better phrase, my bad!
  19. R

    Another convergent and divergent

    And for the setup of the improper integral, try looking at the previous thread where I helped you, at the bottom of my last post. And because I'm going to bed right now and you seem like you really do need some brushing up on your series, here's the work for it step-by-step! {\lim...
  20. R

    Another convergent and divergent

    The comparison test does show divergence that's right. For the integral test however, since the numerator contains n^5 and the derivative of the denominator is 6n^5 then you should be able to tell that u-substitution will work like a charm here... Hint: du/u = ln u. And for the setup of the...
  21. R

    Finding a Volume using integration

    Correction: I was not doing calculus, I was finding the area of a single rectangle and in no way, shape, or form finding volume by using known cross-sections. Mark44's hint is what I would say now that I realize what I was trying to do!
  22. R

    Determine whether the series is convergent or divergent

    EDIT: In helping you recognize the pattern, you should first look at the numerator... The numerator is always 1, so you can sort of look beyond that and concentrate on the denominator... Since the first value of the series is 1, you can surmise that the summation probably begins at n=1 or has...
  23. R

    Determine whether the series is convergent or divergent

    Through some induction it can be seen that the summation is: $\displaystyle\sum_{n=1}^\infty \frac{1}{n^3}. Which is in the form of a p-series: $\displaystyle\sum_{n=1}^\infty \frac{1}{n^p}. So if you were to know the rules of the p-series I assume it would be pretty straightforward
  24. R

    Programs Change Majors, Lose Scholarship?

    I suppose the answer you were looking for is that I was very into computers and everything about them (programming, engineering, design), and thus applied for the scholarship. Since applying however I've (as many do I'm sure you're quite aware) decided that it's not for me, and don't wish to...
  25. R

    Programs Change Majors, Lose Scholarship?

    Correction: "this scholarship that I'm highly competitive for." And I would assume I'm "highly competitive" based on my qualifications as a committed high school student along with the various accolades I've received and the motivation I've demonstrated. And no, this was not intended to be a...
  26. R

    Programs Change Majors, Lose Scholarship?

    Hence the post asking for others' advice, thanks. Also, I will not be majoring in anything I can't stand, period.
  27. R

    Programs Change Majors, Lose Scholarship?

    Well I've been programming and involved heavily with computers for around 5 or so years, and took AP Comp Sci and made a 5 last year, and all was well, I was on track for Comp Sci/Comp Eng in college. And then I went to 2 separate colleges for visits and set up to attend Comp Eng classes while...
  28. R

    Programs Change Majors, Lose Scholarship?

    I have been accepted to University of my choosing to study Computer Engineering. However, since I applied I've already discovered in no way, shape, or form, do I wish to study computers at the college level. I'm much more interested in Mechanical Engineering, Mathematics, or Physics, and wish...
  29. R

    Square root day

    this reminds me Pi day is coming up quick and in a hurry... gotta start memorizing again woot.
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