Analysis and Calculus

If, X is a line. X squared is an area. X cubed is a volume. What do you suppose X to the power of four is?

8((sin2a)^2)-4 as a single function of sin(a) or cos(a) sry Chapter final i had no idea about and this was the only one that slipped me.

If a body moves from A to B then before it reaches B it passes through the mid-point, say B1 of AB. Now to move to B1 it must first reach the mid-point B2 of AB1 . Continue this argument to see that A must move through an infinite number of distances and so cannot move. Zeno of Elea 450 BC ?

x->-infinity,lim(x+sqrt(x^2-4x+1)) i can't for the life of me work out why or how it is possible the limit is 2?!?!

I am trying to solve the following problem: Show that | cos x | <= 1, that is, I am trying to show that the absolute value of cos x is less than or equal to 1 for all values of x, assuming that the only thing I know is the series of the function cosine, that is, just using the following I need to be able to solve the problem: cos x = 1 + Sum ( -1)^n (x^2n)/2n! the sum for n = 1 to infinity I am also trying to prove the same results for sin x = sum (-1)^n-1 x^(2n-1) / (2n - 1)! For the cos x, I broke it into 3 parts, one for x < 1, x = 1, x >1. For x < or = 1, we have cos x = 1 + sum (-1)^n* x^2n/2n!, and we know this is the alternating seri…

Yes, this is homework, but it's under the calc section because I'm looking for a discussion more than just quick answers. 1) a) Find the everage temperature, to the nearest degree, between t=6 and t=14 for all [math]F(t)=80-10\cos(\frac{\pi t}{12})[/math] [math]\frac{1}{8}\int_{6}^{14}80-10\cos(\frac{\pi t}{12})dt[/math] [math]\frac{1}{8}[80t+\frac{10\pi}{12}\sin(\frac{\pi t}{12})]_{6}^{14}[/math] [math]\frac{5}{4}[8t+\frac{\pi}{12}\sin(\frac{\pi t}{12})]_{6}^{14}[/math] [math]\frac{5}{4}[8(14)+\frac{\pi}{12}\sin(\frac{7\pi}{6})]-\frac{5}{4}[8(6)+\frac{\pi}{12}\sin(\frac{\pi}{2})][/math] This yeilds 79.5 or so. The only problem [math]80 \leq F(t) …

find derivate of root (2x - 1) using first principles, Thanks for your help.

How do you write the logical symbol for 'not' using latex. The symbol looks like the letter L, only sideways. Thank you And another question. What is the proper symbolic way to refer to the angle between a and b? I know that the following... [math] \angle \alpha [/math] will be read as "angle alpha" and I know that the following... [math] \angle ABC [/math] Indicates that there are three points in a figure, labeled A,B,C, and that the vertex of the angle is the point B. But what is the best way, or proper way, to discuss the angle between a, and b. In other words, I've been writing this... [math] \vec A \bullet \vec B \equiv |…

How would you solve the following problem? [math]\int \frac{1}{{(asin{x}+bcos{x})^2}}, dx[/math] with a and b being constants. I'm pretty sure the answer is [math]\frac{2tan{\frac{x}{2}}}{(-btan{\frac{x}{2}}+\sqrt{2ab+1}+a)(btan{\frac{x}{2}}+\sqrt{2ab+1}-a)}+C[/math], but I want to know how to do it.

I have been trying to find the intergral of [math]Int{Sqrt[x^3+1]}[/math]... maybe you guys can help me. First of all im defining an unknown function M(x) this function has the property of M(x)^3+1=1/M'(x)^2 so by subsituting this function in to the intergral i get the intergral to be equal to the inverse of M(x). Now this really doesnt help much because to solve the differntal equation is in essence just solving the intergral unless i some how am able genterate a series solution which i dont think would be possible and it wouldnt be useful either because i would have to take the inverse of that function anyway. So my only option now is to explore the properties of the…

I want to derive the formula for the inverse Fourier transform. Does anyone know how to do this? Thank you PS: I was looking at this site here , and they talk about convolutions. I don't know if convolutions would help or not. I remember using the convolution theorem, but it's been awhile.

Hello again! I know it's been rather a while since the last thread, but I'm hoping that someone's still out there I know there's been a fair amount of demand for this to continue, so I plan on posting another few at least. I really must apologise for my absense; things have been happening rather fast around here recently! So, this lesson is all about properties of the derivative and what you can do with it. I feel this may blend a little into the next topic I planned to cover, but nevermind. The answers from last time's post are all in the previous thread - if they're not, just ask me for them. Some properties Right. So, we've gone off and differentiated …

In another thread, yourdadonapogos asked whether or not [math] \frac{\partial}{\partial t} = \frac{d}{dt} [/math] Dave didn't want to answer it in that thread, because that thread is devoted to ordinary derivatives, but I think the question is a good one. Does anyone know the answer? Regards

I want to refresh my memory of fourier series. Can anyone explain what a Fourer series is for me? Thank you

Can someone express for me the relationship between the two. I want to do some review. Also, I don't know what latex symbol can be used to represent the Laplace transform, so I'd like to see that. And also the symbol for a Fourier transform as well. Thanks PS: I used to use the Gamma function all the time, but I forget it now. I could google it, but I'd rather discuss it here.

agghh i hate this kind of maths mainly because i am really bad at it "this kind" being of course the proving of limits using deltas and epsilons can anybody help me or give some advice with this stuff? Cheers Sarah

How does [math]\frac{4^n}{3^{n-1}}=4\left(\frac{4}{3}\right)^{n-1}[/math]?

I am having a problem with this particular problem: Integrate pi(sin(x)^2 - (1/2)^2) from pi/4 to pi/2 I used a trig identity and got this: pi [ (x/2 - sin(2x)/4) - (1x/4) ] however when I evaluate this from pi/4 to pi/2 I am not getting the correct result. Any help is much appreciated. steve

Does anyone have any idea how i can find the antiderivative of cos3/2x in terms of simple functions? The result is [math]\frac{\sqrt \cos{x}}{1/2}[/math]. Ive been playing with it, cant really get anywhere. I was trying to figure out a way with trig identities to simplify it, but I can't get rid of the square root. Maybe using Jacobi's elliptic functions will solve the problem.

Hi there guys! this one's interesting but got me stumped. How would i show that the values of x at which sinxe^(-sinx) has stationary points form an arithmetic sequence? Thanks!

Does anyone know how to use the finite discrete difference calculus to find a formula for the following finite sum? [math] \sum_{n=1}^{n=m} n^2 [/math] Thank you

I have a question about derivatives. Is there any step in the definition of a differential of time,dt, which mathematically stipulates that the flow of time is unidirectional, or does the mathematics of the "unidirectionality of time" have to come from the thermodynamical concept of entropy? Thank you

In my revision on linear algebra i came across this statement. If a continuous function is invertible then its inverse need not be continuous! except i am having a hard time finding examples. Can someone give me such a function. cheers.

The arithmetic sequence a, a+d, a+2d, a+3d,...., a+(n-1)d has the following properties: When the first, third, and fifth and so on terms are added, up to and including the last term, the sum is 320. When the first, fourth, seventh and so on terms are added, up to and including the last term, the sum is 224? What is the sum of the whole sequence? Im clueless, can ne1help. Thx alot.

#1 the integral from -infinity to +infinity of the function: e^-(x^2) #2 the general integral of the function |x^n| not written as two integrals btw i'm looking for an ALGEBRAIC method, not a graphical method