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1. (‡) Prove asymptotic bounds for the following recursion relations. Tighter bounds will receive more marks. You may use the Master Theorem if it applies. 1. C(n) = 3C(n/2) + n
Introduction: "Mathematical literacy is an individual's capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments, and t
A piece of cardboard in the shape of a trapezium ABCD & AB || DE, ∠ BCD = 900, quarter circle BFEC is removed. Given AB = BC = 3.5 cm, DE = 2 cm. Calculate the area of remaining p
I had just come back from a very interesting talk arranged by a Mathematics Centre, it was aimed at parents of primary school-going children. They had talked about, and demonstrate
We have independent observations Xi, for i = 1, . . . , n, from a mixture of m Poisson distributions with component probabilities d c and rates l c, for c = 1, . . . ,m. We decid
If the p th , q th & r th term of an AP is x, y and z respectively, show that x(q-r) + y(r-p) + z(p-q) = 0 Ans: p th term ⇒ x = A + (p-1) D q th term ⇒ y = A + (
I gave my niece a whole heap of beads and showed her how to divide it up into sets of 10 beads each. Then I showed her how she could lay out each set of I0 beads in a line, and cal
what are rctilinear figures ? types of rectilinear figures and their propertiees.
It is difficult to produce the individual answers and the insights that they were providing. But, let's look at some broad patterns that we found, which are similar to those that o
Find out if the following series is convergent or divergent. Solution There really is not very much to these problems another than calculating the limit and then usin
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