Analysis and Calculus

lighting quick question.... how do you show this? i dunno how to include abs values and stuff.... Thanks Sarah

It might sound like a stupid question but when not dealing with logs is it ok to integrate 1/x into INX? The reason i ask is because the course i am doing right now does not directly state that this applies to all cases ie when not dealing with natural logs involving INX, ie: 1/x dx= INX (1) and INX dx= XINX-X (2) So, is (1) true for all cases?

Hi everyone! Recently, in our calculus class, we solved some related rates problems, and I decided to think of one myself. Then I figured out that its not as easy as it seemed! Maybe someone can give me a helping hand in it: So, here's how it goes: A roll of paper of thickness 0.1 mm (you can assume any numbers, really) is pulled at a constant rate of 20 m/min. How fast does it radius decrease around the radius of 5 cm (in other words, what is dr/dt?). I made several assumptions to simplify the problem, but they didn't help much: for example, the minimum radius is 0, and the paper is unrolled not spiral-like, but in concentric circles with increasing radiuses …

sorry to bother everyone but i found a question to which i never learned process so i wonder if anyone can tell me da rules or explain it to me [math]f(x)=e^{2x)[/math] find [math]f^6(0)[/math] though i think this is a fundamental technique I must have missed it when they were teaching it. so i checked the book and it said the answer was 64 now the only way i could get it to equal that, is to find the derivative [math]\frac{dy}{dx}=2e^{2x}[/math] then solve f(0) [math]f(0)=2[/math] then i thought that [math]f^6(0)=(f(0))^6[/math] so i did [math]2^6=64[/math] i'm not sure if my process is right (which i think it isn't cuz it didn't…

Hi there, This is my first post here, so please dont bite my head off. I have a problem here, over time I have a equipment with I need to monitor. I was thinking of using CUSUM to detect a upward or downward trend. I have been using the CUSUM, which I have not been able to get to work. Can anyone point me in the right direction? Sample Data: 591.7753 593.463 587.9513 587.8231 592.0743 591.9248 580.8374 588.1008 582.2474 591.1344 589.639 589.9167 582.5037 597.2656 592.0743 588.5281 584.3837 589.0408 588.7631 583.3156 581.5424 588.3785 595.2147 599.0387 599.5941 598.4832 597.9705 596.5819 593.3134 589.4467 599.8718 586.4345 584.7041…

hey can i just check if i have done this problem right.... For which values of the constants a, b and c is the function f(x) = (x − a)/(bx − c) self inverse? i get for c = 1 a = any real number and b = any real number how'd i do? Thanks Sarah

hey again Show that f(x) = |x|^3 is differentiable at every real x, and find it’s derivative. i am not sure exactly what the question means by "show".... i got f'(x) = 3x.|x| (not even sure if that right but anyways) and i suppose that f'(x) is defined for all R numbers of x.... however i dont think thats really "showing" anything anyones thoughts on the matter would be welcomed Cheers Sarah

[math]y=e^{sinx}[/math] find [math]\frac{dy}{dx}[/math] i know it equals [math]e^{sin(x)}cos(x)[/math] very easy question but my teacher did it out in her haed so i want to see the right prosess

Can someone show me how to compute the radius of convergence of the following power series? [math] \sum_{n=0}^{n=\infty} \frac{nx^n}{2^{n+1}} [/math] There are different ways to do it. Regards The first term is zero, so [math] \sum_{n=1}^{n=\infty} \frac{nx^n}{2^{n+1}} = \sum_{n=1}^{n=\infty} \frac{n(n-1)!x^n}{(n-1)!22^{n}} = \frac{1}{2}\sum_{n=1}^{n=\infty} x^n \prod_{k=1}^{k=n} \frac{k}{2(k-1)} [/math] So [math] f(k) = \frac{k}{2(k-1)} [/math] In the sum, n goes to infinity, hence k goes to infinity. The product from k=1 to n, of f(K), gives the nth coefficient of the power series. So in the limit we have: [math] \lim_{k \to \in…

how do you show/prove that a function is differentiable at EVERY real x?? lol i just cant figure out the method? i thought of induction but yeah....guess not anyways yep that it Sarah

How do you know what limits to put when double integrating. For example for the joint probability distribution function [math]f(x,y)= \begin{cases} 2 & \mbox{if } 0 \leq y \leq x \leq 1\\ 0 & \mbox{elsewhere} \end{cases} [/math] we want to calculate the marginal probability density function of X which is [math]f(x)=\int_{-\infty}^{\infty}f(x,y)dy = \int_{0}^{x}2 dy = 2x[/math]. How come 0 and x are used as limits? Why couldn't we have picked, say, 0 and 1?

Can anyone help as to how to solve the following differential equation ? (x+2)y' - (2x+5)y = -2x3 - 3x2 + 4x (figures after variables meaning powers) Just a beginner in differential equations so might look very trivial to some of you but I would like to demonstrate the solution rather than just see that it works... solution is C(exp(2x))(x+2) + x2 where C integration constant First part of solution is found easily and it then amounts to integrating (-2x3-3x2+4x) / (((x+2)2)(exp(2x))

due tomorrow, oh how i hate procrastination.. need to solve y''=2y+2tan^3x anywho, i know about the parameter thing, but how do i solve y''=2y....just use the charactoristic equation r^2=0? seemed to easy... edit**figured it out

From example 2: I can kind of understand the method used but i just don't know why that once the product rule has been used there is no way to just integrate the 2 terms. I know that it is the same term that we started with and that it has just been left in its integrand notation to keep things simple, i think that is correct. I have written on the RHS what i think the method is i would just like to know if i am on the right track, which if i am not is not really surprising to me

Because if you start out with the equation: 1^1 = 1^0 (1)Log 1 = (0)Log 1 1 = 0 Or did I do something naughty?

[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.

Is the following derivation correct? We want so compute the sum of the following infinite series: [math] 1+x+x^2+x^3+x^4+....x^n+... [/math] If x is greater than one, the series clearly diverges, but the interval where x is greater than or equal to zero is not so clear. Assume that the series is convergent, and the sum is S. Therefore: [math] S = 1+x+x^2+x^3+x^4+....x^n+... [/math] Therefore: [math] xS = x+x^2+x^3+x^4+....x^n+... [/math] Therefore: [math] S-Sx=1 [/math] By the distributive axiom of algebra: [math] S-Sx=S(1-x) [/math] By the transitive property of equality, it now follows that: [math] 1=S(1-x) [/math]…

Theorem: [math] \frac{d(A+B)}{dt}} = \frac{dA}{dt} + \frac{dB}{dt} [/math] To prove the theorem, it suffices to prove the following statement is true: [math] d(A+B) = dA + dB [/math] It suffices, because if the previous statement is true, and dt is nonzero, then we can divide both sides by dt, to obtain the theorem we are attempting to prove. Let [math] Q = A+B [/math] Thus, we are attempting to prove that: [math] dQ = dA + dB [/math] Definition: [math] dQ \equiv Q2-Q1 [/math] Where we have used subtraction to define the differential of quantity Q. Q1 is the value of Q at one moment in time, and Q2 is the value of Q at the v…

Okay, can someone help me with this little puppy? [math]\lim_{x\to0}(\frac{1}{sin x}-\frac{1}{x})[/math]

This is not a calculus question, but rather a question about calculus. I was watching some very bright kids the other day really enjoying calculus. I have to admit playing with symbols and numbers is not my favourite pastime. When you look at a calculus equation what do you see? Do you see a series of approximations of the real world. Like when I see the sentance “the cat played with the ball ”, I see a picture of a cat playing with a ball. I do not see the letters or the words. I was wondering ,when you read a calculus equation do you picture, spheres being intersected by planes? or lines folding out to become planes and then extruding to becom…

Does anyone have an idea how to prove the following: [/url] [math] h(A\cup B, C\cup D) \leq \max\{h(A,C), h(B,D)\} [/math] with the Hausdorff distance. I can see it on a drawing, but I'm not able to prove it correctly. Thanks in advance

I have been taught to do it this way: Say i wish to integrate. (2x+1)^1/2 dx 1) u=2x+1 2) therefore... u^1/2 dx 3) du/dx= 2 4) u^1/2 du/2 (because du/dx=2) 5) therefore...1/2 u^1/2 du. At step 5 the integration is then performed, i have no problems with that. It says in the book that du/dx=2 should not be split up to make du/2=dx, but this is what is done anyway in all the examples Note, the only reason this is done in the first place is because u are …

is it possible to have multiple integrals of the same function for instance when you differentiate a function like f(x)g(x) then you get f(x)g'(x)+g(x)f'(x) but then integrating that function becomes integral of (f(x)g'(x)+ integral of f'(x)g(x) which is most certainly not f(x)g(x)

Solve the differential equation dy/dx = (x^2)(y^2) with the condition y = 3 when x = 0. i get y = -3/((x^3)-1) so how'd i do?

hey everyone i dont really understand this example in my text book, i've never seen anything asked like this before.... anyways if someone could please explain what they are doing, it would be greatly appreciated Sarah