Analysis and Calculus

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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?

What is 'my' in calculus?

While reviewing basic calculus, I noticed that the curve (1+t^2,t^2,t^3), which clearly has a cusp at (1,0,0), has a derivative curve (2t,2t,3t^2) which is clearly smooth. This struck me as odd since differentiation usually seems to turn cusps into discontinuities, whereas integration smoothes out a curve, especially a curve described by polynomials. In fact, in general I have always taken a curve to be smooth iff it has a continuous derivative, which this curve has, and yet a cusp cannot be smooth in any sensible sense. I suspect the explanation is relatively simple - just something I'm missing. Thx in advance.

Just a little food for thought kinda thread here; what ways are there to find the numerical value of "e", that is, the natural base. There's 2 I learned this semester: 1. 1/1! + 2/2! + 3/3! + ... n/n!, as n-->infinity where n is an element of natural numbers Or something like that and 2. The fundamental limit of calculus, that is: lim x-->infinity for (1 + 1/x)^x

In this paper (see attached, last hint on the page included): "theta < kappa" means "theta is equivalent to <kappa" because "|P(theta)| = 2theta <= |H(kappa)|". Is this wrong?

Richard Feynman, one of the pioneer of quantum electrodynamics, said the following formula was "the most remarquable of Mathematics". It is a simple formula, anyone having studied the rudiments of complex numbers will find it obvious. Personally, I find it beautiful because all the symbols of mathematics I love the most (for now, i'm a beginner ) are gathered together : the transcendent [math]\pi[/math] and napier constant, [math]i[/math] : square root of the polynomial [math]x^2+1=0[/math] in C, the equal sign and the two neutral elements : 0 and 1 for the binary operators addition and multiplication. [math]e^{i\times\pi}+1=0[/math] What do you think about it ?

Hi, Here is a math question : First I'm going to define some things (some names may already exists that I don't know of, so please take my definition into consideration) - let's call p[n] the nth-rank prime number p[0]=1, p[1]=2, p[2]=3, p[3]=5 etc - as you know, each integer >0 can be written as a product of integer powers of prime numbers.. let's call it the "prime writing" of a number... i'll write u[n] so for any integer X we have X = product( p[n] ^ u[n] ) - we can extend this to rational numbers, simply by allowing u[n] <0 My question is : can we define a set of irrational numbers in ]0 ; 1[ that extends p[n] when n<0 and are t…

A cool little example of common confusion with partial derivatives, from Penrose's "The Road to Reality" (he attributes the words in the title to Nick Woodhouse.) Let's consider a function of two coordinates, f(x,y), and a coordinate change X = x, Y = y + x Because the X coordinate didn't change and is the same as the x coordinate, one could expect that the corresponding partial derivatives are the same, fX=fx. And, because the Y coordinate is different from the y, these partial derivatives, fY and fy, could be expected to differ. In fact, this is just opposite: fX=fx-fy fY=fy The confusion is caused by the notation: fX does not mea…

Here's a problem I recently came across in a very old calculus book. Unfortunately, it was an even-number, and I can't quite figure out for sure how to solve it. A bag of sand originally weighing 144 lbs is lifted at a constant rate of 3ft/min. The sand leaks out uniformly at such a rate that half the sand is lost when the bag has been lifted 18 ft. FInd the work done lifting the bag this distance. The thing about it is this would be easy to solve, except that we don't know the weight of the bag *alone* and can not just assume that it's negligable. I know that the work is force times distances, and that you use infinite sums to find the work over that particul…

I noticed some unexpected behavior in the real-valued f(x)=(1+x)^1/x, as a function of real numbers, when plotting it on wolfram alpha. I inputed: plot (1+x)^1/x from x=-0.0000001 to x=0.0000001 and saw that it unexpectedly seemed to oscillate near zero. I took a closer look with: plot (1+x)^1/x from x=-0.00000000001 to x=0.00000000001 and saw that it definitely seems to oscillate near zero. My original rough graph on paper using a hand calculator suggested the curve was smooth near zero, and even windows calculator's 32 decimal places were unable to reveal the oscillation when I manually calculated many different values near zero. I don't think f(x) i…

What is the most elegant (simple or natural) solution of the equation a+8b+27c+64d+125e=0

A % change for stomach patients within a year from 300 to 360 is: [math] \frac{360-300}{300}*100= [/math] 20% A % change for liver patients within a year from 200 to 260 is: [math]\frac{260-200}{200}*100 =[/math] 30% Hence Total % change in stomach and liver patients within a year is: [math] \frac {620-500}{500}*100=[/math] 24% But it should be 50% shouldn"t it ??

is it infinity or 1 or 0 or N.D???? Bro plzzz help meeeeeeeeeeeeeeeeeee

Is 1 + 1 + 1 = 3 ? and are there alternative answers ? like for instance 2.99999999999999999999999999999999999999999999999999999999999999999999991

There was a post a while back on "1/0", and I was disappointed to see a post of mine deleted. So I'll be brief and repeat my previous remark. While 1/0 is generally undefined for fields, it is defined on the Riemann Sphere for the so-called extended complex numbers. On this complex manifold, 1/0 = [tex]\infty[/tex], the "point at infinity". Wolfram|Alpha and Mathematica implement this sort of complex arithmetic, albeit a bit inconsistently. Here's what Wolfram|Alpha thinks 1/0 is: http://www.wolframalpha.com/input/?i=1%2F0

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?????

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[math]\displaystyle \lim_{n\rightarrow 0}\frac{\log_{2}\sum_{k=1}^{2^n}\sqrt{k}}{n}[/math] [math]\displaystyle \lim_{n\rightarrow 0}\frac{\log_{2}\sum_{k=1}^{2^n}\sqrt{2k-1}}{n}[/math] I have had people give me the results after plugging it into Mathematica/Maple, but I was wondering if anyone knew how to solve these without a computer.

Hello, I need to find a two-arguments function u(x,y) which satisfies six constraints on its derivatives. 1&2: On the first derivatives: du/dx>0 for all x & du/dy>0 for all y (so u is increasing in x and y) 3&4: On the second derivatives: d²u/dx²<0 for all x & d²u/dy²<0 for all y (so u is concave in x and y) 5&6: On the crossed derivatives: d²u/dxdy<0 for all x+y<theta (or at least y<theta) & d²u/dxdy>0 for all x+y>theta (or at least y>theta) (theta is a threshold) I found one specific function that satisfies those conditions: u(x,y)=xy+1-exp(theta-x-y) But I don't think this is the only …

The MC was pretty easy. But wow...the free response. 1,4, and 5 were easy...they were the ab topics. 2,3, and 6...man. Each problem had at least one part that almost nobody in my class got right. I'd never seen some of those types of problems before. 6c: The differential equation! Omg! Question 3, with the derivitives with respect to y (i got that right...but then converting it to polar and integrating it there!) Also, the parametric questioin might have well just castrated you right there. I'm confident I did well, but I can't imagine how far down they are going to redo the scale. ~Wolf 1. Volume between sqrt(x) and e^-3x 2. parametric with dx/dt =…

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

Can calculus solve the volume of a 3 dimensional object? Like a pile of grain on the ground that is not symmetrical?

What would be the thickness of the coin (disk or cylindrical) with 1 unit diameter that would make the tail /head/body(side) outcome be a fair 1/3 probability?