Analysis and Calculus

Anyone knows how to do these? http://www.math.mcgill.ca/jakobson/courses/ma262/a1.pdf

-y^2-z^2=1.......from this equation, is it a circle or what?? help me anyone!!

2004-06-30 Hello. My name is Hans Lindroth. I have a question about continuity. How do you verify/proove that, for instance, arcsine(x) is continuous? I mean, when I apply the definition of continuity on it I get: 0<=|arcsine(x) - arcsine(a)|<e (e>0) (Here "<=" means "smaller than or equal to"). I'm stuck here however since I don't know of any method to convert "arcsine(x) - arcsine(a)" into something I can modify. Can anybody help me out? If you can, please give me a hint. Thanks Hans Lindroth.

I am a senior in high school (second day), with a background in ap physics and precalculus (i do know some calc though). I have been trying to derive kinematic equations with a dissaptive force involved(ie friction). I have tried a couple of methods...i want to know if i got the right answer first method: first off i assume that the friction is porpotional to the speed(i hear expermentaly it is more -kv^2) [math] y''=a-\tfrac{-ky'}{m_p} [/math] [math]\tfrac{d^2x}{d^2t}+\tfrac{kdx}{m_pdt}-a=0[/math] find the roots [math]x=c_1e^(t(\tfrac{-k}{2m_p}+\sqrt{\tfrac{k^2}{4m_p^2}+a}))+c_2e^(t ( \tfrac{-k}{2m_p}-\sqrt{\tfrac{k^2}{4m_p^2}+a}))[/math] then take the dervative…

From the ‘order of axioms’ in real number analysis, for every [math]\alpha , \beta \in \mathbb{R}[/math], exactly one and only one of the following holds. a) [math] \alpha < \beta[/math] b) [math] \alpha = \beta[/math] c) [math] \alpha > \beta[/math] Then an order for the real numbers can be laid down lexicographically. Let [math]\alpha \in \mathbb{R}[/math], and let [math]\alpha [/math] be expressed in the form: [math]\alpha = a_0.a_1a_2a_3 . . . a_k[/math] Let [math]\beta \in \mathbb{R}[/math], and let [math]\beta [/math] be expressed in the form: [math]\beta = b_0.b_1b_2b_3 . . . b_k[/math] When the first [math]a_k[/math] that diff…

Please, could you help me on finding if the attached equation is always verified? Thank you!

When Schrodinger derived his famous equation, he derived it with the electron in mind, as is obvious with his use of E=p2/2m+V. This is fine if you want to work with electrons, but I wanted to see what the equation would be like if you derived it for the photon, using E=pc. I worked through it and got the equation: [math]\frac{d\psi}{dt} = -c \frac{d\psi}{dx}[/math] Does anyone know how to find a square-integrable solution to this equation?

I was doing some summer calc work and was asked to find the range of the function sqr{x-1}. The book said the answer was infinity but I thought that an argument could be made for sqr{inf-1}. Am I missing something or is this worth getting into? Can't find the LaTeX symbols for sqr and inf either.

Hi, I should probably have named this thread "Challenged New Member". I am 63 and have a highly technical background training and experience. I have joined here for several reasons but one in particular is the apparent number of members that are good in Calculus. I had introductory Calculus 40 years ago but have never used it and at this late stage simply consider that I do not do calculus. I do algebra and write my own engineering and physics programs in GWBasic. But while I understand the functions of calculus I certainly do not perform it. i.e. - I am a handicap! I have my own web site: http://www.unikef-gravity.com/ Which is part of a t…

2004-06-30 Hi. My name is Hans Lindroth. I study maths at the university for the first time and was hoping someone could answer me this. If I'd like to find the limit of, say, xarctan(1/x) lim x->0 How would I do it? I mean, does the function arctan(1/x) go to infinity as (1/x) does (when x->0) or does it just oscillate like arcsine or arccos? If anybody knows, please tell me. Thanks Hans Lindroth.

Hello. My name is Hans Lindroth. I'm studying maths at the university for the first time. This time I have a question of more general type. It goes like this: "show, by using the basic postulates concerning limits of functions, that |x| is a continuous function." How should I approach this problem? If anybody can give me a hint then please help me. Thanks Hans Lindroth.

I have 4 of them 1) An open topped cylindrical glass jar is to have a given capacity. Find the ratio of height to diameter if the area of glass is a minimum. 2) The cost per square metre of the sides of an open topped cylindrical tank is twice the cosr per square metre of the bottom. Find the most economical proportions for a tank of given volume. 3) A rectanglar sheet of iron 300 cm wide is to be bent to form a gutter whose cross section is the arc of a circle. What radius will give the gutter the maximum carrying capacity? 4)Find the dimensions of the circular cylinder of largest volume that can be inscribed in a right circular cone of height H and ra…

Taken from my calculus exam The function f satisfies [math]f(2x)=xf(x)+1[/math] 1)Show that [math]f(0)=1[/math] 2)Show using induction that [math]2^{n}f^{n}(2x)=nf^{(n-1)}(x)+xf^{n}(x) \forall x \in R[/math] 3)Hence, derive the first three terms of the Maclaurin series of [math]f[/math] I managed to do it, but because of 1) and 2) if 3) was given by itself I would think i would be completely lost for some time. edit: [math]f^n[/math] denotes the nth derivative of f

Newbie Group: Members Posts: 5 Member No.: 295 Joined: 26-June 04 2004-06-27 Hello there. My name is Hans Lindroth. I've just started to study maths at the university. Now I've encountered a problem about limits. It goes like this: "In a circle with radius 'R' a chord is drawn, the length of which is 'L'. Let 'H' be the distance between the center of the chord and the center of the smaller arc being cut off the circle by the chord. Decide the limit: lim H/(L^2)". L->0 I've tried by finding an expression for "H" in terms of "L". This doesn't seem to lead me right though. Besides, the answer (which is "1/8(R^2)") is given i…

I've got this question i'm somewhat flumexed with. [math]\int_{e}^{e^2} \left(\frac{5}{x} + e\right) dx[/math] What've i've tried is as follows [math]\int_{e}^{e^2} (5x^{-1} + e) dx = [5ln|x| +e]_{e}^{e^2}[/math] [math] = (5ln(e^2) + e) - (5ln(e) + e)[/math] [math] = (5(2) + e) - (5(1) + e)[/math] [math] = (10 + e) - (5 + e)[/math] [math] = 10 + e - 5 - e[/math] [math] = 5 [/math] which evan i can see from just looking at the graph is wrong, but for the life of my i can't see why. I'm sure i've got everything right after the intergration, but i'm almost just as sure that've i've intergrated it correctly. Any help much appreciated.

Hello, I'm stuck in a convolution question. x(t) = u(t) - 2u(t-2) + u(t-5) h(t) = e^(2t) u(1-t) y(t) = x(t) * h(t) (I'm using capital T as tao and Int as integral from minus infinity to plus infinity) y(t) = Int ( x(t-T) h(T) ) dT = Int ( u(t-T)-2u(t-T-2)+u(t-T-5)[e^(2T)u(1-T)] )dT = Int ( [e^(2T)u(1-T)] u(t-T) ) - Int .... ------------------------------------------ I'm going to set integral limits due to the interval that the step functions are nonzero. So: 1-T > 0 -> T < 1 t-T > 0 -> T < t But the T is smaller than both 1 and t... so.. What do I have to take as integral limits? I'm stuck here. Thank you fo…

Had my Analysis II paper today, and I thought I'd share a nice question with you all Find: a) [math]\lim_{x\to 0} \left( \frac{\sin(2x)\tan(5x)}{3x^2} \right)[/math] b) [math]\lim_{x\to 0} \left( \frac{\sec^{2}(x) - 1}{2x^2} \right)[/math] c) [math]\lim_{x\to 4} \left( \frac{\sqrt{x} - 2}{\sqrt{2x+1} - 3\sqrt{x-3}} \right)[/math] Have fun, I'll post the answers in a bit (in case you were wondering, I think I just about did okay on it )

Hi, For people who use the ti-89 what would you say the advantages and dis-advanatges are from a teachers point of view and a students point of view. From the teachers point of view: -One disadvantage is that the students do not get to learn the method behind the answer, so they will lack in this skill. From the students point of view: -Easy to use -Less work for them What else would you guys say?

Hello , the other day I discover a graphic technique very useful to solve math problems ... It has got foundations of different branches of the knowledge ... There are a few examples of how to solve math problems ahh the technique is "Mind Graph" Best Regards Angel S.P.

I have to say, I'm stumped. I've tried solving this problem but it's being a complete gimp and I'm completely fed up with it. Here it is in all its glory: Use Taylor's theorem to prove that the function [math]f:\mathbb{R} \to \mathbb{R}[/math] given by [math]f(x) = e^{ax}\cos(bx+c)[/math] (for [math]a, b, c \in \mathbb{R}[/math]) can be written as the power series [math]f(x) = f(0) + f'(0) x + \cdots + \tfrac{1}{n!} f^{(n)}(0) x^n + \cdots[/math] for all [math]x\in\mathbb{R}[/math]. Any help is much appreciated as the question is worth 14 marks/25 in a past paper

Can someone clarify or explain what the Fourier Series is? From what I understand, its a way in which periodic funx can be expressed as a sine & cosine funxs together; However, seeing as how my knowledge in Calculus is limited to Grade School Advanced Functions & Introductory Calculus, I'm just like when I see sites like http://www.nst.ing.tu-bs.de/schaukasten/fourier/en_idx.html#DIRI & http://mathworld.wolfram.com/FourierSeries.html

For example, is the interval [0.9999999...., 1] continous? Does it even make sense to ask that question?

So guys, how'd you all do? Did you guys think it was too terrible? I thought the multiple choice was pretty much reasonable, nothing too crazy...and the free responses weren't awful either. Well except for number 5, the one about logistic growth...Yeah, you can't arrest me for talking about it because I'm not being specific. lol, my calc teacher said I could tell him what the topic of it was. OK, well I dunno, just wanted to check up with the rest of the BC calc world, check ya guys later!

not sure if it's in the right section, but hopefully you won't have much difficulties answering this. after seeing a weird hubcap on a vehicle, i had this nagging question, but 1st lets give a little background. on the hubcap, there was a picture of an eagle right in the middle and ofcourse when the wheel spins, the eagle image is reduced to blur. so now my question: how can one make a similar design if at all possible so that when the wheel spins, the image stays in the center and is not affected by the rapid motion(blur) of the rest of the wheel? one of the things i tough might be possible is the create this image like a blur in itself when the …

hey, i did my undergrad in music and english and now am lost beyond reckoning with the impulse response stuff in my postgrad. Could anyone help with these exercises? They're examples from my lecture notes and have no idea how my lecturer got the answers. Please help? Ex.1) Show that x(t)*h(t) = h(t)*x(t) EH? ANY IDEAS? Ex.2) The unit response of a continous system is h(t)=3e -2t-5e -4t/sup]. If the input is modelled as x(t)= [delta](t)-2[delta](t-1)+[delta](t-2.5), find the value of the output at time=1.5s. Ans: y(t)=0.717 at t=1.5s. Ex.3) An electrical system has unit-impulse response h(t)= 3te -4t . If a unit step function u(t) is applied to the system, …