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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 denition 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!)
MAKING CONNECTIONS : you have read about what the ability to think mathematically involves. In this section we shall discuss ways of developing this ability in children. As yo
Joey has 30 pages to read for history class tonight. He decided in which he would take a break while he finished reading 70% of the pages assigned. How many pages must he read befo
Proof of: if f(x) > g(x) for a x b then a ∫ b f(x) dx > g(x). Because we get f(x) ≥ g(x) then we knows that f(x) - g(x) ≥ 0 on a ≤ x ≤ b and therefore by Prop
(a) The generating function G(z) for a sequence g n is given by G(z) = 1 - 2z/(1 + 3z)3 Give an explicit formula for g n . (b) For the sequence gn in the previous part co
Find the 35th term of the sequence in which a1 = -10 and the common difference is 4.
The number of seats in each row can be modeled by the formula C_n = 16 + 4n, when n refers to the nth row, and you need 50 rows of seats. (a) Write the sequence for the numb
ABCD is a trapezium AB parallel to DC prove square of AC - square of BCC= AB*
9:59-10:45
Example of Integrals Involving Trig Functions Example: Estimate the following integral. ∫ sin 5 x dx Solution This integral no longer contains the cosine in it that
Before taking up division of polynomials, let us acquaint ourselves with some basics. Suppose we are asked to divide 16 by 2. We know that on dividing 16 by
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