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A) Prove the following theorem by considering two distinct cases. For any integer n, n^{2} + n is even.
B) If x = r^{2 } - s^{2} and y = 2rs for any integers r and s, then x^{2} + y^{2 }= z^{2} for some nonnegative integer z. State the hypothesis of this sentence and the conclusion. Give a direct proof of the statement
Prove that the Lagrangian coef?cient polynomials for p n (x) satisfy ∑ n k=0 l k (x) = 1. Hint: It is only a 3-line proof. Consider the interpolating polynomial for a constan
parabola
APPLICATIONS OF LAGRANGE''S MEAN VALUE THEORM?
y''(x)=2*10^-6*y(x)(100000-y(x))
The data of the table below give details of the components, prices and standard quantities used in making a kind of chemical. Measure the composite index with 2007 as base year us
. The Government of Uganda wants to locate a refinery plant that will annually receive crude oil from two wells in Bunyoro region, F1 and F2. The refinery plant will process the cr
Draw concentric circles of radii a and b, each centered at z=id (on the imaginary axis). Suppose φ(x,y) is a harmonic function inside the washer defined by these circles. The circl
the solution of diffusion equation by using separation of variables
PROCEDURE OF TRACING A CLOSED LOOP
A young couple requires RM30000 for an overseas trip which they want to make in six years time. How much they have to invest now at 18% p.a. compound interest compounded monthly, t
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