Analysis and Calculus

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Hello, my name is Calleigh and i am new to the forum! I am in Calculus II and have a few questions on some problems. I am using the textbook Calculus 8th edition by Larson, Hostetler and Edwards. Could someone please help me? The problem is on pg 959 in chapter 13.8 in the text, number 56. It reads: a. Find the absolute extrema of the function. b. From the form of he function, determine whether a relative maximum of a relative minimum occurs at each point. and it gives: f(x,y)=2x-2xy+y^2 and R:The region in the xy-plane bounded by the graphs of y=x^2 and y=1 What does it mean when it states f(x,y)??? I've already heard of f(x). I don't know what it mean…

Hello, my name is Calleigh and i am new to the forum! I am in Calculus II and have a few questions on some problems. I am using the textbook Calculus 8th edition by Larson, Hostetler and Edwards. Could someone please help me? The problem is on pg 950 in chapter 13.7 in the text, number 46. It reads: a. Find symmetric equations of the tangent line to the curve of intersection of the surfaces at the given point. b. Find the cosine of the angle between the gradient vectors at this point. c. State whether or not the surfaces are orthogonal at the point of intersection. And they give: z=x^2+y^2, and x+y+6z=33 and the pt (1,2,5). My first problem is unders…

Hello, my name is Calleigh and i am new to the forum! I am in Calculus II and have a few questions on some problems. I am using the textbook Calculus 8th edition by Larson, Hostetler and Edwards. Could someone please help me? The problem is on pg 942 in chapter 13.6 in the text, number 76. It reads: The temperature at point (x,y) on a metal plate is modeled by: T(x,y)=400e^-((x^2+y)/2) where x>=0 and y>=0. It asks to find the directions of no change in heat on the plate from the point (3,5). It also asks to find the direction of greatest increase in heat from the point (3,5). Does anyone know what this problem is talking about? Usually it helps if …

Hi everyone, i have a midterm exam tomorrow night (Thursday night) and i'm looking at problems in the section of the book to help myself prepare. Can anyone answer this question for me? I have attempted to answer this problem but without the answer i don't know if i'm right. 1. Find the angle theta between vectors r(t) and r'(t) as a function of t. 2. Sketch the graph of theta(t) 3. Find any extrema of theta(t). 4. Find any values of t which the vectors r(t) and r'(t) are orthogonal. and they give vector r(t) = t^2 ii + t ij And there are no typos, that's really what the question asks. First off, i have NO idea what ii and ij mean, i'm assuming they …

Hi everybody! I would like to ask you an opinion. I have a file with time variable quaternions and I would like to numerically evaluate the time derivative, that is given q(i), q(i-1) t(i) and t(i-1) I express the quaternion time derivative as q_dot = (q(i) - q(i-1)) / (t(i) - t(i-1)) where q denotes a quaternion and t is the time. Now my question is: do I have to express the time in a quaternion form [t(i) 0 0 0] and use the quaternion division or can I divide a quaternion by a scalar? I know there is a formula linking the angular velocity to the time derivative of the quaternion, but I don't know the angular rate which has to be determined using this fo…

I've heard people say that all ciphers (speaking of substitution/translation) are crackable, especially with brute force (supercomputers). I bet 1000 bucks I can make a code that will be impossible to "crack". Here's how it will work. I will make a small book that will explain how to encode/decode the gibberish. It will have what letter translates to what, etc. Then, I will write a paragraph, page, (an excerpt from a book, or anything in the english language) with my code. I'll give you both the english text and the code. Then i'll give you the code to a new paragraph, and you have to figure out what it says. .... you won't be able to. But: someone with the little bo…

Given z=f(x,y), how would I go about finding the inverse function(range) like it was done for f(x)=y,when f(x)=x^2-1 ,for example,we would put x^2-1=y and solve for x?

In the converted substituation form of /int 12x^2 (x^3 +1)^5 dx, u du = a. 3x^2 (x^3+1) b. 4 /int u^5 du c. 3u^2 (u^3 +1) d. 3x^2 My guess was b.

Below is three example study quesitons for an upcoming calculus test and I'm trying to see if I have the answers correct, please advise... Thanks 1. If d(d) is a position equation, then what does d''(t) = 0 represent? 1. The object described by d(t) is stationary (v(t)=0) 2. The object described by d(t) is neither accelerating nor decelerating (a(t) = 0) 3. The object is at the origin (d(t) must be 0 for d''(t) to be 0) 4. None of the above. MY GUESS IS (4) 2. Forward Gaussian Elimnation is to the _____ method as backwards Gaussian Elimination is to the _______ method. 1. induction, substitution 2. addition, substitution 3. induction,…

So, it is commonly accepted that the first three dimensions are those that we experience every day (e.g. length, width, and depth). And that the first dimension is linear, the second to do with area, and the third to do with volume. The fourth, however, is sometimes called duration, meaning that it represents "time". Often it is conceived as also linear (such phrases as "timeline" exemplify just that). So my question is as follows; is this "cyclical" nature of dimensions inherent or conceived? I imagined at first that it would be like [math]\i^n[/math] in that it repeats every four integral values but then I realised that this conception was probably largely fabricated by…

I need to take the Fourier transform of a product of three terms. The statements I have of the convolution theorem are thus: [math]\frac 1 {2\pi} \int dk F(k)G(k)e^{ik x} = \int du f(u)g(x-u) . [/math] How do we express the inverse, namely: [math] \int dx f(x)g(x)e^{-ik x} [/math]? Can I just follow my nose and write a similar convolution integral in k-space?

I have been trying to teach myself calculus in part by reading the tutorial. I have a few questions and was wondering is someone could give me some guidance. Is there a difference when you use the [math]\cdot[/math] or [math] \times[/math]? I understand where you get this: [math]\frac{d}{dx}u \cdot v + \frac{d}{dx}v \cdot u = \frac{d}{dx}(x-2) \cdot (x + 4) + \frac{d}{dx}(x+4) \cdot (x - 2)[/math] But I do not understand how you go from that to: [math]1 \cdot (x + 4) + 1 \cdot (x - 2) = (x + 4) + (x - 2) = 2x + 2[/math] I think I might understand how to do it when I do not use the chunking but I want to learn how to use the chunking method. …

this info is from my dad: my uncle is a math major. he used to explain to my dad how 1+1 does not equal 2. he would go through the steps, but my dad would never see any twist. my uncle lives in california, and i don't feel like calling him in the middle of the night to ask him. so how does 1+1 not equal 2?????

Hey guys, After a VERY frustrating semester (work was tough, professor wasn't very helpful, and very big workload), I got a B+ in my math course. I don't like it at all, but it's better than failing, so I'm good. I have the exam sheet still, and I would REALLY want to know where I screwed up. I have scribbled the answered that I put up in the actual exam on the edges of the questions, and I'm probably going to post lots of mistakes (it was stressing ) -- but I would like to know the answers. I know it's not something we usually do here, solve questions, usually we ask to give the WAY -- well, feel free to give me a way too. I am going to post the questions an…

It is well known that in general the quintic algebraic equation is not solved algebraically. It means that the inverse function of quintic polynomial is not expressed algebraically. However we also know some functions which are not elementally functions are expressed with nonlinear differential equations. Then is it possible to express the inverse function of quintic polynomial with any nonlinear differential equation? I tried to induce such nonlinear differential equation in the following site; http://hecoaustralia.fortunecity.com/stbruno/stbruno.htm

I find the following confusing. I compared the two Wikipedia articles with each other: http://en.wikipedia.org/wiki/Newton%27s_method and http://en.wikipedia.org/wiki/Newton%27s_method_in_optimization The first one tells us that with [math]f'(x_{n}) = \frac{ \mathrm{rise} }{ \mathrm{run} } = \frac{ \mathrm{\Delta y} }{ \mathrm{\Delta x} } = \frac{ f( x_{n} ) - 0 }{ x_{n} - x_{n+1} } = \frac{0 - f(x_{n})}{(x_{n+1} - x_{n})}\,\![/math] then [math] x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}\,\! [/math] No restrictions what so ever as to the choice of [math]x_0[/math] (the initial value). However, the second one, uses the Taylor expansion of [math]f(x)[/math] …

Intergrate by parts: ∫ x(x +1)^4 dx X . ∫( x+1)^4 - ∫(∫(x+1)^4) . dy/dx (x) X. (X+1)^5 /5 - ∫(x+1)^5 /5 . 1 X. (X+1)^5 /5 – (x+1)^6 /30 +C. This is the best I can go. Our A’level teacher says its fine to do it till here, but the book has simplified answer I want to get to. Could someone tell me how to reach to the answer of (5X-1)(X+1)^5 /30 + C. Help appreciated !

I need to find a function that can be proved using calculus techniques. I have used every local source of information to find a method to work this out but alas... the answer eludes me. Heres the question: Following 5 point lie on a function: (1,20) (2,4) (5,3) (6,2) (10,1) Find an equation that passes through these points and has all the following: 3 points of inflection At least 1 local minimum and local maximum At least one Critical point (eg max/min/intercept etc) is not at a given point The curve is continuous and differentiable throughout The equation is not a single polynomial, but must be a piecewise-defined function Now I know that theres go…

Hello! I was wondering if someone can give me a functions that increases gradually in the beginning, and then picks up an exponential rate after some time. It would be much similar to an exponential function such as x^2, but it would increase gradually for a certain time in the beginning. Thanks!

I am stuck with the following which comes from an attempt to find acceleration in polar coordinates. The velocity in the x direction is [math] V = cos\phi dr/dt - sin\phi (r d\phi/dt) [/math] and I need to find dV/dt so I think I need [math]\delta V/\delta r \ and\ \delta V/\delta \phi [/math] Then I have terms like [math] \delta (dr / dt) \delta r[/math] which I dont know how to handle. I have a book which gives the same formula for V and then the answer on the next line - I cannot "join the dots"! Have spent a bit of time looking on the internet but only found a different answer to the one in my book - could not get that either. Any help apprecia…

Hi i'm looking for a general solution for [math]\phi(t)[/math] here . [math]\int \ t^n \phi(t) \, dt = \left( \int \ t \phi(t) \, dt \right)^n ; n=0,1,2,3 ...[/math] any help is appreciated ..

Let R be the shaded region by the graph of y = lnx and the line y = x -2, as shown above. a) find the area of R

Can someone explain to me why [math]\frac{dP(t)}{P(t)}=r \, dt[/math] becomes [math]\log |P(t)| = rt + C[/math] when integrating on both sides? It's the left side that is my problem. The right side is understood.

Hello, I have 9 means for 9 separate samples. I would like to compare them (with a software) to know if they are significantly different. What test(s) should I use? A Student t-test for mean comparison? Can it be done with Excel, as it's the only software I've got right now? But if it can't be done with Excel could you show me how to do it with SPSS? Thank you for your help.