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...
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...
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...
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...