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Values from the iteration x = cos(x) are:
x0 = 0.8, x1 = 0.696707, x2 = 0.766959, x3 = 0.720024, x4 = 0.751790, x5 = 0.730468.
a) Calculate the sequence {yn} from Aitken's ?2 method. Given that the solution of x = cos x is 0.739085133 . . . , ?nd the rations between consecutive errors in {xn} (which approach a constant A) and also in {yn} (which approach another constant, say B). Con?rm that {yn} is converging twice as fast as {xn} (i.e. that B = A2).
b) Use Steffensen's method: from x0, x1, x2 calculate y0. Then start the iteration again from x3 = y0, and from x3, x4, x5 calculate y1.
A new gantry crane for a metal fabrication shop is to be designed. The designer has proposed the following two different configurations: A. Using only truss elements B. Using the
a restrained steel bar is heated from 20 degrees to 194 degrees and not permitted to expand. the bar is 10mm diameter, determine the thermal stress in the bar
for what values of (a,b) does the point P (0,a,b) lie on the line through Q (1,-1,4) and R (2,3,5)?
An electronic module is mounted on a machine and is modelled as a single degree of freedom spring, mass, and damper. During normal operation, the module of mass m kg is subject to
Produce a discrete time series y(t i ) by super positioning 5 cosinusoidal components, for your own choice of the amplitudes (a j ) and frequencies (f j ). Add some Gaus
definition of trigonometric function #Minimum 100 words accepted#
Arrianna spended $5,500 at 7.5% p.a. compounded quarterly for 'n' years. At the end of 'n' years, Arrianna got back $12,000. What is the value of n? (Approximate your answer in yea
Use Lagrange interpolation to estimate f(3), given that f(1) = 1, f(4) = -3, f(2) = 0 and f(-1) = 3.
As with the first order system, there is a general differential equation that governs the response of a second order system. The equation is of the form: Where: So
b) State by inspection (i.e. without performing any formal analysis) all you can about each of the periodic waveforms shown in FIGURE 1 in terms of their Fourier series when analys
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