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The functions
{sinmx; cosmx}; m = 0,....∞
form a complete set over the interval x ∈ [ -Π, Π]. That is, any function f(x) can be expressed as a linear superposition of these with a unique set of coecients. For f(x) = x, we have
To show that the above holds for x = 1, study the dierence between the left- and right-hand sides of the equality as a function of the number of terms included in the sum. Write an octave program to compute and plot the truncated sum approximation (expansion vs x) for n =4 and 16 together with the function x. Make a table showing the error (dierence between two sides) for n =1, 2, 4, 16, 64, 256, 1024. Plot the result of the expansion for 2 values of n together with the original function. Comment on your results. You should submit an octave script or function le I can use to reproduce your results and a separate document (plain text le preferred) for your comments.
find the simple interest on Rs. 68,000 at 50/3 per annum for 9 month
Linear Equations - Resolving and identifying linear first order differential equations. Separable Equations - Resolving and identifying separable first order differential
how to change order and variable in multiple integral
. The Boeing Company makes a number of different types of aircraft for the commercial airline industry, e.g., the 727, 747, 757, 767, and 777 jet models. Is there any way for Boei
Total Contribution per Year for next 10yeras =$1000+$800 =$1800 So Total Future fund Vaule =$1800*(1+1.073+power(1.073,2)+ power(1.073,2)+ power(1.073,3)+ power(1.073,4)+ power
Simplify following. Suppose that x, y, & z are positive. √ y 7 Solution In this case the exponent (7) is larger than the index (2) and thus the fir
Two tanks initially contain 100 liter liquid each. Their initial concentration are listed in the Figure below. At time zero, the input and output valves are opened simultaneously w
3v2
1.Verify Liouville''s formula for y "-y" - y'' + y = 0 in (0, 1) ? 2.Find the normalized differential equation which has {x, xex} as its fundamental set. 3.6Find the general soluti
y=f(a^x) and f(sinx)=lnx find dy/dx Solution) dy/dx = (a^x)(lnx)f''(a^x), .........(1) but f(sinx) = lnx implies f(x) = ln(arcsinx) hence f''(x) = (1/arcsinx) (1/ ( ( 1-x
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