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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!)
If A, B are acute angles and sinA= cosB, then find the value of A+B. Ans: A + B = 90 o
Find out if each of the subsequent series are absolute convergent, conditionally convergent or divergent. Solution: (a) The above is the alternating harmonic ser
HOW MATHEMATICAL IDEAS GROW : In this section we shall consider three aspects of the nature of mathematical ideas, namely, that they progress from concrete to abstract, from part
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what is the importance of solid mensuration?
Let G be a group acting on a set X. The action is called faithful if for any g ≠ 1 ∈ G there exists an x ∈ X such that gx ≠ x. That is, only the identity fi xes everything. Prov
Find the derivatives of the following functions a) y = 5x 4 +3x -1-x 3 b) y = (x+1) -1/2 c) y= e x2+1 d) y= e 3x lnx e) y =ln(x+1/x)y
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#questionShow that the system oscillates in simple harmonic motion demonstrated by; , for which the general solution where X = (x – x0)..
Determine y′ for xy = 1 . Solution : There are in fact two solution methods for this problem. Solution 1: It is the simple way of doing the problem. Just solve for y to
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