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Assume that (X, d) is a metric space and let (x1, : : : , xn) be a nite set of pointsof X. Elustrate , using only the de nition of open, that the set X\(x1, : : : , xn) obtained by removing every xi from X is open in X. (Sketch a picture to get some intuition!)
examples
The lower portion of a hay stack is an inverted cone frustum and the upper part is a cone find the total volume of the hay stack.
In these problems we will begin with a substance which is dissolved in a liquid. Liquid will be entering as well as leaving a holding tank. The liquid entering the tank may or may
20 equations that equal 36
Solve the subsequent differential equation. 2xy - 9 x 2 + (2y + x 2 + 1) dy/dt = 0 Solution Let's start off via supposing that wherever out there in the world is a fun
Raul has 56 bouncy balls. He puts three times as many balls into red gift bags as he puts into green gift bags. If he puts the same number of balls in each bag, how many balls does
1. Discuss lyapunov function theory and how it can be used to prove global assmptotic stability of solutions.(Give an example form natural and engineering sciences.) --- Draw le
Limits The concept of a limit is fundamental in calculus. Often, we are interested to know the behavior of f(x) as the independent variable x approaches some
5x-2y+55x=4x
Here are four problems. Four children solved one problem each, as given below. Identify the strategies the children have used while solving them. a) 8 + 6 = 8 + 2 + 4 = 14 b)
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