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The integral
has an exact answer, viz., sinc(pfT). As T®¥ the sinc function tends to zero. Divide the region from -T/2 to T/2 into N equal parts and sum the rectangles on bases Δt =T/N , showing that
Observe that this function is periodic. For a given choice of f and T construct a table to show by how much the discrete version of the integral differs from the true value. Does inclusion of only half the areas of the end rectangles make much difference? Note that you have included N+1 points in your sum. What happens if you have only N points, i.e., if you do not include one of the end rectangles. A geometric construction may assist.
(i) Test for the existence of regression (the F-test). Carefully de ne the null and alternative hypothesis, and explain the result of any R output you obtain. (ii) Which of the
Valid objective function for a LPP with x,y,z as decision variables
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
Define a mapping from the x,y plane to the u,v plane by u = 2x + y, v = -x +2y . If a temperature function is given in the x,y plane by T(x,y) = x+y, what is the value, to 3 de
From this point on it is assumed that any problem amenable to solution with the aid of the Discrete Fourier Transform (or DFT) will in fact be treated computationally with a fast r
How to solve the problems
A company manufactures an assembly consisting of a frame, a shaft, and a ball bearing. The company manufactures the shafts and frames but purchases the ball bearings from a ball be
if u=x^2-2y^2, v=2x^2-y^2 and x=rcosp ad y=rsinp, find the value of the jacobian d(u,v)/d(r,p)
Values from the iteration x = cos(x) are: x 0 = 0.8, x 1 = 0.696707, x 2 = 0.766959, x 3 = 0.720024, x 4 = 0.751790, x 5 = 0.730468. a) Calculate the sequence {y n } fr
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