Recent content by EstimatedEyes

Okay, I assume that a,b, and c are the elements to which you are referring. Obviously a and b are comparable with c but I am having trouble showing that it then follows that a is comparable with b. I know it can't be this easy, but I don't completely understand why c is not already an upper...

Homework Statement Let L be a partially ordered set. Every countable chain in L has an upper bound. Let S be a countable subset of L such that for arbitrary a,b in S there exists a c in S such that a (less-than-or-equal) c and b (less-than-or-equal) c. Prove S has an upper bound in L...

Thanks! Is it possible to generalize that e^(-1/x^2)/x^n as n->0 (n>2 and an integer) also approaches 0?

I don't quite understand what you're asking; Both go to zero and I don't understand how one can do so first...

Homework Statement It is part of a larger problem, but the only hangup I have had is computing this limit. lim x->0 e^(-1/x^2)/x^3. It's to show that the function f(x) = e^(-1/x^2) (when x is not 0) and 0 (when x is 0) is not equal to its Maclurin Series. I know that if I can show that the...

Homework Statement A block of mass m1 = 3 kg rests on a table with which it has a coefficient of friction µ = 0.54. A string attached to the block passes over a pulley to a block of mass m3 = 5 kg. The pulley is a uniform disk of mass m2 = 0.4 kg and radius 15 cm. As the mass m3 falls, the...

Homework Statement A stick of uniform density with mass M = 8.6 kg and length L = 0.7 m is pivoted about an axle which is perpendicular to its length and located 0.24 m from one end. Ignore any friction between the stick and the axle. What is the magnitude of the vertical component of the...

Homework Statement Evaluate the integral of xarctan(3x) from 0 to 0.1 by expressing the integral in terms of a power series. Homework Equations The Attempt at a Solution I differentiated xarctan(3x) until I got two functions that I could turn into power series (arctan(3x) and...

Oh, I proved the second part of your post in part a of the problem and did not realize that it was involved in any way; thanks!

Homework Statement Let f(x) = a_{1}\sinx + a_2\sin(2x) + ... + a_Nsin(Nx) where N\geq1 is an integer and a_1, ... , a_N \in\Re. Prove that for every n = 1, ... , N we have a_n = \frac{1}{\pi}\int{f(x)\sin(nx)dx} with the integral going from -\pi to \pi (sorry I don't know how to write...

Homework Statement Let f(x) = ax^2 + bx + c a,b,c are real numbers f(0) = 1 and \int\frac{f(x)}{x^2(x+1)^3}dx is a rational function. Find f'(0) Homework Equations The Attempt at a Solution f(0) = 1 = a(0)^2 + b(0) + c c = 1 f'(x) = 2ax + b f'(0) = 2a(0) + b = b I tried to integrate...

Homework Statement Determine whether the series is convergent or divergent by expressing s_{n} as a telescoping sum. If it is convergent, find its sum. \sum\frac{3}{n(n+3)} Homework Equations The Attempt at a Solution Partial Fraction Decomposition: \frac{1}{n} - \frac{1}{n+3} Partial Sum...

I just figured out that the distance was from the lens so I kept getting it wrong because I was using the eyes value that they gave.

Homework Statement A farsighted woman breaks her current eyeglasses and is using an old pair whose refractive power is 1.655 diopters. Since these eyeglasses do not completely correct her vision, she must hold a newspaper 39.4 cm from her eyes in order to read it. She wears the eyeglasses...

\int{\frac{u^2}{\sqrt{a^2 - u^2}}}