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Along with giving us a technique to compute antiderivatives, integration by parts is very important theoretically. In this context, it can be thought of as a technique for moving derivatives off of one function and onto another. To see what we mean, suppose that f(x) andg(x) are functions with f(0) = g(0) = 0, f(1) = g(1) = 0 and with continuous second derivatives f''(x)and g''(x). Use integration by parts twice to show that the integral from [0,1] of f''(x)g(x) dx = the integral from [0,1] of f(x)g''(x) dx.
A train traveling at a speed of 95 mi/h approaches an observer at a station and sounds a 525-Hz whistle. What frequency will be heard by the observer? Assume that the sound velocity in the air is 1090 ft/s.
What is a mathematical model? Explain in your own words. What are some examples of mathematical models that we can use when working with quadratic functions? (Minimum 300 words).
We already saw this for nfinit which accepts either a polynomial or an nf. It will be true for ideals, ideles, congruence subgroups, etc. Ok, let"s stick with elements for the time being. How does one go from one representation to the other?
a rectanlgar playground is to be fenced off and divided into 2 by another fence parallel to one side of the playground. 480 feet of fencing is used. find the deminisons of the playground that maximizes the total enclosed area. what is the maximum ..
In a sample batch of 36 mechanical pencils it is assumed that 10 are defective. If 5 mechanical pencils are randomly selected, what is the probability that none of them are defective?
use double integrals to find the volume of the tetrahedron bounded by the planes x+2y+3z=6, x=y, z=0, y=0
Find the height and radius of the largest right circular cylinder that can be out into a sphere of radius (square root of 3).
The scores on a lab test are normally distributed with mean of 200. If the standard deviation is 20, find
Using GEOMETRY ONLY, for an equilateral triangular region, for which points is the sum of the distances to the sides of the triangle minimal? Please show me and do not point to a web site.
Assume that f(z) is analytic at the origin and f(0) = first derivative of f at 0 = 0. Prove that f(z) can be written in the form f(z) = [z^2]g(z), where g(z) is analytic at z = 0.
Let G be a group (finite or infinite) and let a and b in G. Let o(a) represent the order of a. Suppose G is abelian and both a and b are of finite order. Show that ab is of finite order and o(ab) divides o(a)o(b).
A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How many movies need to be rented each month for the to..
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