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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.
There are many situations which call for the replacement of an integral by a sum, or vice versa. In the former case the highest accuracy is sometimes required. This means that in t
Use Lagrange interpolation to estimate f(3), given that f(1) = 1, f(4) = -3, f(2) = 0 and f(-1) = 3.
simple problems on partial derivatives
Draw parallel lines with slope +1.05; one passes through (0,a), and the other passes through (0,b). Suppose φ is a harmonic function between the two lines, with φ = 0 on the line t
An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars
What is the characteristics of divison
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
Answer the following set of simultaneous equations using elimination or substitution method. a) x-y +z= 10 b) 3x+y+2z=34 c) -5x+2y-z=-14
I. The inventory of records of BeBop Distributing reflected the following for October 2012: Date Transaction Units
Use the simplex method to solve the following LP Problem. Max Z = 107x1+x2+2x3 Subject to 14x1+x2-6x3+3x4=7 16x1+x2-6x3 3x1-x2-x3 x1,x2,x3,x4 >=0
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