# Calculus

- Elementary functions. Calculating limits, derivatives and integrals. Optimization problems
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 Meta Thread / Thread Starter Last Post Replies Views Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions... Feb23-13 10:24 AM micromass 1 37,520 I believe I have a new method of proof for an already existing theorem. The theorem itself is quite elementary and the... Dec18-05 01:18 AM mathwonk 41 12,228 Hi all! Here's something I'm having difficulty seeing: Suppose u_n > 0 and \frac{u_{n+1}}{u_n} \leq... Dec18-05 06:14 AM Muzza 4 3,986 Suppose you have a unit circle in the complex plane e^{it}, -\infty \leq t \leq \infty. The contour will wind around... Dec19-05 03:28 PM Jonny_trigonometry 11 1,189 Finding the center of mass of a two dimensional object of constant density is a question that frequently occurs on my... Dec20-05 12:06 AM Tide 8 8,578 So I'm writing a paper involving Gamma and Beta functions, Dirichlet integrals, Generalized Hypergeometric functions,... Dec20-05 07:39 AM benorin 12 1,935 (This isn't homework :redface:) Does this series converge? {\sum\limits_{n = 1}^\infty {\left} } Does this... Dec20-05 08:04 AM matt grime 1 1,488 Ok, so I would like to formally settle this one. I have a sequence of sets C_{N}^{n}\subset\mathbb{R} ^{n},... Dec20-05 04:30 PM benorin 0 3,242 (This isn't homework, just a curiousity derived from another problem) Well, this is probably quite simple...:shy: ... Dec20-05 05:24 PM bomba923 3 1,473 Imagine that I have a pipe that is on a constant slope at any percent. On the low end of the pipe, there is a... Dec23-05 05:11 PM Tide 1 8,065 let,s suppose that we have the limit with n tending to infinity: \frac{f(n)}{g(n)}=1 then i suppose that for n... Dec25-05 05:32 PM matt grime 4 1,550 for a divergent series i can write an expression in the form: \int_{R}dxC(x)w(x)e^{-ax} where a is a divegent... Dec25-05 05:43 PM Tom Mattson 1 1,588 Let's say I wanted to find the length of the perimeter of a semi-circle using integration with x(t) = cos(t) and y(t)... Dec26-05 12:36 AM Alkatran 3 1,251 I'm not getting this. Can someone show me how they got from this: - T cos ( \theta ) + (T + \Delta T ) cos (... Dec26-05 04:59 PM lalbatros 15 2,139 let be the next functional differential equation: \delta{F}=G then its solution would be: F=\int{DG ... Dec27-05 11:39 AM matt grime 3 1,500 i would like to know how to prove this equality: \frac{1+2^p+3^p+.....+n^p}{\int_0^{n}dxx^p}\rightarrow{1} for... Dec27-05 03:39 PM mathwonk 3 1,369 Working from "Principles of Mathematical Analysis", by Walter Rudin I have gleaned the following definition of... Dec27-05 03:47 PM mathwonk 6 1,446 Hi, I want to do an experiment using two dissimilar ropes in my basement and see if I can produce some results using a... Dec28-05 11:50 AM Cyrus 7 1,971 let be the divergent series: 1^p+2^p+3^p+.....................+N^p=S(N) with p>0 my question is..how i would... Dec28-05 03:17 PM shmoe 2 1,436 If f is a continuous decreasing non-negative function on a_n = \sum_{k=1}^nf(k) - \int_1^nf(t)dt. I need to show... Dec29-05 02:15 PM ex-xian 3 2,492 I found this in the web: We say that f is lower semi-continuous at x_0 if for every \epsilon > 0 there exists a... Dec29-05 03:39 PM benorin 10 2,023 Facts: 1. We have the decrecient sequence {a_n} which converges to "a". 2. Let "K" be a constant. 3. We have the... Dec31-05 11:41 AM Castilla 4 1,756 I'm not sure if this is calculus, but it is like a review in my calculus class. Suppose that in any given year, the... Jan2-06 05:41 PM Jacobpm64 9 2,433 let,s suppose we have a function f so the limit when \epsilon\rightarrow{0} is infinite..now i would like to know how... Jan5-06 05:21 PM Edwin 2 1,203 My Calculus professor has indicated a 'shortcut' in determining polynomial fraction limits, I am inquiring if this... Jan6-06 09:57 AM VietDao29 2 12,251 Hi, Let C_1 and C_2 be nonempty convex sets and suppose C_1 \cap C_2 \neq \emptyset . I read a text that claims... Jan6-06 11:19 AM matt grime 10 2,065 Hi. I have this exam in vector calculus tomorrow, but i'm having trouble sorting the following formula out. Could... Jan8-06 03:55 PM Tide 3 1,777 It should be relatively easy, but I can't seem to figure out how to begin.. if anyone could help me out, I would be... Jan8-06 05:00 PM Demian^^ 0 883 My calculus book describes the following example: Equation: \lim_{x \rightarrow 0} \sin \frac{\pi}{x} = \text{does... Jan9-06 07:13 PM Data 15 2,089 I'm doing a review in calc I to prepare for calc II. I'm now applications of derivatives (optimization). Okay so when... Jan10-06 05:24 AM Demian^^ 4 1,671 Find a & b for the following transformation 1/(z+a) = (a/z) + I am kind of lost as to where to start on this... Jan11-06 12:16 AM Tide 1 1,830 Given a real-valued function f:X \mapsto \mathbb{R} where X is a subset of \mathbb{R}^n. Consider a closed extended... Jan11-06 02:12 AM kaosAD 0 974 I am thinking about purchasing some math software so I can get a better understanding of the math I am learning. I... Jan11-06 10:52 AM shmoe 19 2,929 I would like to determine necessary and sufficient conditions for equality to hold in Minkowski's Inequality in... Jan12-06 10:17 AM fourier jr 2 7,404 (A, B) is an interval in the real line. If I take the middle point (B-A)/2, and then take the middle point of each of... Jan13-06 10:30 AM Castilla 7 1,317 Hello...I need help and I know this is a very simple problem...I don't know why I'm getting stuck( Maybe because it's... Jan14-06 01:45 PM matt grime 1 956 How do you find the limit to: Lim x->0+ sqrtx/(1-cosx) I use the L'Hopital rule and i get lim x->0+ ... Jan14-06 04:35 PM mathwonk 12 1,601 This problem is baffling myself and several of my friends in the infamous Physics 152 class... so I give it to you... Jan15-06 12:09 PM matt grime 5 1,462 I have made some observations regarding the Precise Limit Definition. For any given polynomial: ax^n The... Jan16-06 12:03 AM benorin 10 2,033 Hi, I ran into a situation I haven't experienced before where the integral of the derivative doesn't get me the... Jan16-06 01:33 PM dc20 6 1,149 f_n(x)= x^n/1 + x^n does this series converge on the interval Say if x = 1 then the series is < some epslon ,... Jan17-06 02:16 PM maverick6664 4 1,210

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