Determine convergent series
Suppose that An >or = 0 for every n belonging to N and sum An is convergent series. Prove that sum a^2 n (a squared n) is also a convergent series.
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Suggest the piecewise constant interpolation of the function f(x)=sin(x), 0 <= x <= 381, at points x_i = ih, where h = 0.1. Thus, our interpolant satisfies v(x) = sin(ih), (i-0.5)h <= x < (i+0.5)h, for (i = 0, 1, ..., 3810).
Discuss how the Principle of Inclusion-Exclusion yield the Sum Principle?
A 120 I tank initally haves 90kg or salt dissolved in 90 I of water. Brine containing 2 kg/I of salt flows in the tank at the rate of 4 I/min and the well-stirred mixture flows out of the tank at 3 I/min. Determine an equation f
Determine the ratio of the fluxion of x to the fluxion of 1/x using Newton's "synthetic" method of fluxions.
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Assume we are given the set A where set A = {1, 2, 3}. How many elements are contained in the Cartesian Product A X A? Give an example of a relation, selected from A x A, that satisfies the reflexive and anti-symmetric properties.
Could a 4x7 matrix have dim Col A=5 and dim Nul A=2? Justify your answer. Remember to think about the possible pivots in rows and columns.
Let the ralation R be stated on the set Z of all integers by a R b if and only if a^2-b^2 is multiple of 3. Find out whether R is an equivalence relation. Either prove that R is an equivalence relation or specifically demonstrate which properties
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