Analysis and Calculus

I didn't like approximate definitions of trigonometric functions (it was about 34 years ago). Then I made speculation that side of angle (if angle is less or equal to Pi/2 rad) proportionally divides arc Pi/2 and its chord (21/2). Then my math teacher corrected me with her speculation that there is especial arc in which if to connect any two points of proportional division of this arc and its chord by straight line and to connect any two points of any another proportional division of this arc and its chord by another straight line , then the straight lines cross in one point of definition of trigonometric functions and angles(arcs). Is there any prize for exact definitio…

Hi everyone. Tina here. This is my first ever post on such a forum and would apologise in advance for my lack of formal clarity and perhaps very amateurish presentation etc. But I have a burgeoning interest in the beautiful mystery and potential of mathematics and reason in general. And would love that anyone might direct me in my latest field of curiosity, which is....well...."things to do with primes." I may not be able to formalise my question very well....as intimated....and do understand in general that people often may not even be sure what they are asking.. But here goes.... Consider, if you would....…

Hello, I've been getting into the concept of hyperreal numbers lately, and I've got tons of questions. What I understand about the hyperreals is that they are numbers larger than any real number or smaller than any real number. I'm sure you can imagine how counterintuitive this sounds to someone like me who's new to the concept. It's like talking about numbers greater than infinity. I always thought that was impossible. So it shouldn't be surprising that someone like me would have a ton of questions. I'll start with a couple. 1) Assume that R is a hyperreal number greater than any real number. What does 2 x R equal? It's clear what 2 x n means where n is a real …

Is it possible to define the second derivative of f(x) in this way: \[ f''(x) = \frac{f(x+2dx) -2(f+dx) + f(x)}{(dx)^2} \] I am using a finite difference approximation called "Second order forward" from the link, I use dx instead of h: https://en.wikipedia.org/wiki/Finite_difference#Higher-order_differences

I have heard that they can be found online with answers but no explanations. I can only find free response questions. Help please...

When you perform the expression n! (read "n factorial"), you multiply all the positive integers between one and n. They have to be positive, so n>0, but they also have to be integers, so you would think that factorial of a decimal is impossible. However, when I put it into my computer's calculator, I do get a real answer. For example, .01! = 0.99432585119150603713532988870511..., and 2.1! = 2.1976202783924770541835645379483..., so there must be a way to perform a factorial of a decimal. What is it? How do you do that?

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?????

:pi:/2 :int: sin(4x)dx 0 :int: sin(ax)dx = -1/a cos(ax) right? so . . . . . . . . . :pi:/2 -1/4 cos(4x) | . . . . . . . . . 0 [(-1/4) cos 4:pi:/2] - [-1/4(cos 4(0))] (-1/4) - (-1/4) 0 ?? where did I go wrong

I ran into a coin flip problem where flipping 4 coins has a 6/16 or 3/8 probability of landing 2 heads and 2 tails. I expected this value to be 1/2, because you have a 50% chance of getting heads or tails. Then that is only 6 of the possible 16 outcomes, instead of 8. Then I realized that the number of possible outcomes where there is an even number of heads and tails actually decreases, compared to the total possible outcomes, the more times you flip the coin. I was wondering if someone could, please, troll me about the reason why this doesn't disprove the mathematics of probabilities, since the outcome of flipping more and more coins in a row approaches closer a…

Hey I just want to find out if anyone knows if it is possible to enter complex numbers into a matrix of a scientific calculator. I have a CASIO fx-991ES PLUS scientific calculator. For example: If 20cos(200t -45)= 70jI1 + 90jI2 .....1 and 0=2jI1 +8jI2 ....... 2 Is there any way to solve these equations in a 2x2 matrix on a calculator? (The j's are imaginary, used so that there is no confusion with the variable vectors of I1 and I2). It is easy to solve these equations by hand but when it gets up to 4 equations to solve it gets far more tricky and time consuming. I am getting fed up with all the math that is involved to solve simple circuits, so I t…

Not sure if this the right place for the question. Please move this post if not. Is there anyone here able to help me understand how R's Z-function is used to create his famous landscape? I will never understand the Z-function but am happy to treat it as a black box. What I'm trying to grasp, among other things, is what numbers have to be used as inputs in order to produce the necessary outputs. My thought is that each output value must have an input value associated with it. Yet I've never seen a discussion of the inputs, only the outputs. So maybe I'm misunderstanding something very basic. Just a discussion in natural language would be fine. I am no…

Area of Circumscribed (around a circle) n-gon = n/tan[(n-2)(180)/(2n)] square: Find: As, pi Given: r=1, n=4 As=n/tan[(n-2)(180)/(2n)]=4/tan[(4-2)(180)/(2x4)]=4/tan[2(180)/8]=4/tan45 = 4 hexagon: Find: Ah, pi Given: r=1, n=6 Ah=6/tan[(6-2)(180)/(2X6)]=6/tan[(4)(180)/12]=6/tan60 = 3.464 decagon: Find: Ad, pi Given: r=1, n=10 Ad=10/tan[(10-2)(180)/(2x10)]=10/tan[8(180)/20]=10/tan72 = 3.249 hectagon: Find: Ah Given: r=1, n=100 Ah=100/tan[(100-2)(180)/(2x100)]=100/tan[98(180)/200]=100/tan88.2 = 3.14263 chiliagon: Find: Ac Given: n=1000 Ac=1000/tan[(1000-2)(180)/(2x1000)]=1000/tan[998(180)/2000]=1000/tan89.82 = 3.…

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.

My (overlong?) title describes the problem completely; my question is how? I realise that there can be multiple [sic] answers; I'm after the smallest integers that produce c. eg. Given 1.05; A/B = 21/20.

Hey guys, I could really use some hints on how to solve the integral [math] \int \frac{x}{1+\sqrt{x}} dx [/math] I tried some substitutions, and doing some manipulations on the expression, with no solution. Any help would be much appreciated. Regards, Kerbox

Can anyone help in finding the integrating factor of (ydx-xdy)=0 According Schaum's outline of differential equations 3rd edition it's integrating factor are (-1/x^2), (-1/(x^2+y^2)). plz help me. May God bless those who will help me.

If y=x + sin(xy) then dy/dx equals.... I don't understand how you take the derivative of sin(xy). I think you have to use the multiplication rule and get x dy/dx + y But what do you do from there?

How would I find the area shaded in blue below? (please forgive how big the image is) I'm assuming you'd have to use calculus as there is no way to simply subtract the area of the circle from the area of a larger rectangle without ending up looking for a limit. I guess I don't know how I'd go about finding the anti-derivative of a circle.

Can you please check if my answer is correct. [math] y=sin(sin(sinx)) [/math] [math] y'=cos(sin(sinx))cos(sinx)cosx [/math] (My calculus professor doesn't want our answers simplified.)

So, can anyone solve for y in terms of x? yx=xy I sure can't solve it, and my TI-89 couldn't solve it either.

I might have already posted this in this forum quite some time ago, but the problem just came back to me, and now I want to solve it again, or at least know the solution. Here it is, more in depth: Arc length of a spiral Say you are givin a spiral with an initial radius r' (read r-prime), where r' is any real number greater than 0. As the radius "spins" it grows at the same rate as it "spins". So for every degree it rotates, the radius gains 1/360th of it's initial length (r'); exapmle- if r' = 1 cm, after 90 degrees the new radius is 1.25 cm, then after a full revolution it is 2 cm. And this goes on for however many revolutions. What I need it a solution fo…

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 was reading a post on ar15.com, and thought it was a great discussion, ended up being 11 pages of math. so here is the question? X=.99999999999 repeating 10X = 9.9999999999 repeating 10X - X = 9X 9X = 9 X = 1 Therefore .9999999999 repeating = 1 So is this an example of limits?

prove : -0=0

So I got this HW assignment and i was wondering if anyone could confirm my anwser. Here's the question: The population, in thousands, of Mathville is modeled by the equation P(t) = 20(4t+3)/(2t+5), where t is the time in years since 2005. The question is...what is the population growth rate in 2006. So then I took the formula and found the first derivative, which i found to be 280/(2t+5)^2, and then set the first derivative to equal 0 so i could solve for t. In the end I got 0 = 280. Now i know that doesnt seem right. Can anyone help me? PS- on the following question i concluded that the population will never reach 50000 because there is a horizontal asymptote at y=4…