Analysis and Calculus

Starting in September next year I will be taking AP Calculus. Hopefully I won't need to bug you guys, but it's good to know you're here I was just wondering if you know of any good online resources that could get me started now. I figure that if I have a head start it will be a lot easier to handle next year when I have lots of other classes along with it. Of course, I also need to prepare for the AP test!

This is an extra credit problem for my calc class, and I doubt anyone in my class will get it. Please help, as I am also clueless. Ellipse E is centered at the origin, and has a horizontal minor axis of length 4. If you rotate the portion of E which falls only in the first and second quadrants about the x-axis, the resulting rotational solid has volume 800pi/27 . Find the length of E's major axis without using a calculator.

As a question last class our prof threw this one to us; Use the intermediated value theorem to show that there is some angle theta radians btw 0 and pi that sintheta=theta + 1 After looking at this however either I'm missing something really basic or this problem isn't right. No angle theta would fufill that equation because sin can only be 1, so theta would have to equal 0, and sin(0) isn't 1. Is there something I'm missing or did the prof mess up?

I am having a difficulties finding an example of an open set U c R and a continuous function f that map R to R such that f(U) is not open.

Hi all - I'm crap at this stuff but I desperately need to solve this one: d^2y/dt^2 = d^2y/dr^2 + (1/r)dy/dr I need to obtain an expression y(t,r). If anyone can help or at least direct me to some easy to follow tutorial you'll make of me a happy man. Peace all J

does anyone know of a good book with which to study 2nd year calculus? I'm almost done with a book on first year calc

OK, so I have several questions... First, a differential is a tangent to the curve and the integral is the area between the curve, X axis, and differentials...right? Second, if I have [math]y=mX^n + b[/math] it would be: [math]y=(mn)X^{n-1}[/math] for a differential, right? And [math]y=(m/n)X^{n+1} + b[/math] for an integral...right?!

[math]\frac{dy}{dx}=\cos(y+f(x))[/math] here y and f are functions of x . highly non linear. tried maple. didnt give jack

you can only use it to find the area underneath the curve if f(a) is equal to zero correct? nevermind found my answer

Could somebody explain to me begining calculus, such as calc 101. I'd like to know things like the difference between differential and intregal calculus, and how to use them.

Hello! My D.E. exam is tomorrow, and I was wondering something (but don't have the time to try it myself). Say you have a first order diff. eq.: e.g. M(x,y)dx + N(x,y)dy = 0 Now, say that one method to solve it in y is to use the homogenous method, then seperating (i.e. y = v(x)*x, dy/dx = ...) Could an integrating factor solve this equation too (in general)? More specifically, an integrating factor w/rt to only one variable, either some u(x) or u(y) [such that Mu dx + Nu dy = 0 is an exact D.E.]. Thanks!

Hey guys, can someone help me with the following proofs: Prove that the sum (1/n^p) for n=1 to infinity converges for p>1. Also, can you help me in proving the ratio test, that is suppose that x_n > 0 for all n in N (N = set of natural numbers) and suppose also that lim sup ( x_n+1/x_n) < 1, then prove that the series x_n for n = 1 to infinity converges. Then if lim inf ( x_n+1/x_n) > 1 then the same series x_n diverges.

Let [math]f\colon \mathbb{R}^{2}\to\mathbb{R}[/math] given by [math]f(x,y)=\frac{xy^3}{x^2+y^6}[/math] if [math](x,y)\ne (0,0)[/math] and 0 if (x,y)=(0,0) Question asks me to use the definition or partial derivatives to show that f_x and f_y both exist at (0,0). and at any other point (x,y) i can do the first part, but for the second part i cannot simplify the expression for the limit.

I need to find out where the functions are increasing/decreasing has local extrema where the graph is concave up or concave down, asymptotes and coordinate intercepts. Thanks ahead of time.

CAN ANYONE PLEASE PROVIDE ME WITH THE PROOF OF THEOREMS ON LIMITS OF FUNCTIONS?

This is the question which I cannot do and it's driving me nuts : A power house, P, is on one bank of a straight river 200m wide and a factory , F, is on the other bank 400m downstream from P. The cable has to be taken across the river under water at a cost of $12.00/m. On land the cost is $6.00/m. What path should be chosen to minimize the cost? This may be easy for some but I AM DYING so all help is appreciated! Thank you in advance -Diz

Hey all. I'm doing the following for an assignment in my Calc class, and I just need some help finishing up the problem. I'm having trouble with #1 of the first project here: http://www.math.washington.edu/~m124/Stewart5Eprobs/appliedproject.pdf I have looked at it, analyzed it, figured out a lot of stuff about the problem, but I just can't put it all together to get a final polynomial. I have things listed out such as the derivative of P(x) = 0 at x = L and x = 0 and other various conditions I believe to be true. I just can't put it all together. If any of you can help with this last step in acquiring the answer to this problem, it would be greatly appre…

A question was posed in our calc class about how the general formula for the taylor series expansion of arcsin was created. Here is the general formula: I tried calculating each derivative. But after the fifth one, it got too long and I still couldn't see a pattern. Here is a readout from the ti-89 f (0) = 0 f` (0) = 1 f`` (0) = 0 f```(0) = 1 f^4 (0) = 0 f^5 (0) = 9 f^6 (0) = 0 f^7 (0) = 225 = 15^2 f^8 (0) = 0 f^9 (0) = 105^2 ? So I was wondering if any of you could help me in trying to find how the general formula was created. thanks

Can someone quickly tell me what the integral of 1 over e^y(x) is I have a seperable DE im trying to solve. Pook (:

If you have f(x) = e^(-.25x + 2) is the derivative e^(-.25x + 2) ? If not, what is it?

Can you help me with the following problems plz. I have a course in telecommunications and i have to understand complex numbers first. I can't solve the following exercises: 1) Write in the form z=x+jy the complex number e^e^j ^=exp 2)how i can solve this equation |z+2|=|z-1| and what is the algebraical explanation (z=|z|e^jè|)

Prove the triangle inequaltiy as follows a) [ math ]|z_{1} + z_{2}|^{2} = |z_{1}|^{2} + |z_{2}|^{2} + (z_{1}Z_{2} + z_{2}Z_{1})[ /math ] (b) [ math ]z_{1}Z_{2} + z_{2}Z_{1} = 2Re (z_{1}Z_{2})[ /math ] [ math ]<2|z_{1}Z_{2}|\[ /math ] [ math ]=2 |z_{1}][z_{2}|\[ /math ] Where capital Z's are the conjugate, Oh and < means greater than or equal to Cheers

this is a Q i'm having trouble with...can some1 help me out? PT is the tangent at P, a variable point on the parabola xsquared = -16y. If T lies on the directrix, find the locus of the midpoint PT. what i've already gathered is that the directrix must be y=4. I'm not sure if P's coordinate is (-4tsquared, 8t) because the parabola isn't in the form ysquared = 4ax but for the coordinate of T, all i know is that its y value must be 4. Can any1 tell me wat im missing?

f(x) = (x+3)(x-3)/(x+2)(x-2) This yields 6 quadrants with a parabola-like curve in the middle. The curve isn't a parabola, correct? How do you locate the center of this curve? f(x) = x/(x+2)(x-2) The inner graph looks like x^3. Is its center the origin?

The question is fine a equation f(x) that has a vertical asymptotes of X=1and X=3 and a horizontal asymptotes of Y=1 A) (x-1)(x-3) / y-1 = x^2-4x+3 / x-1 OR B) (x-1) /(x-1)(x-3) = just the oppsite of above is any of these correct? I think B is correct but right now I can't find any info on it in my book