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Some techniques for computing the mathematical constant e=2.71828... accurately need infinite series. An infinite series is the sum of the terms of an infinite sequence. As we cannot find the sum of an infinite series by a computer, we approximate this sum by creating and summing as much element as we can. The speed of this process can be increased using a parallel computing approach. Approximate the e using Maclaurin Series given as:

Please approximate e using Maclaurin Series using any of the libraries that you know (MPI, PTHREAD or OPENMP) (I have these files)Attach your code, and snapshots of all the results to this exam paper. Try at different numbers of processors and numbers of samples, and compare the results.

[login to view URL] way of finding an approximation to π is to use numerical integration such as:

ease approximate π using the integral given above as a sum of rectangles and using any of the libraries that you know (MPI, PTHREAD or OPENMP) Attach your code, and snapshots of all the results to this exam paper. Try at different numbers of processors and numbers of samples, and compare the results. Attach your code, and snapshots of all the results to this exam paper. Try at different numbers of processors and numbers of samples, and compare the results.

Suppose we toss darts randomly at a square dartboard, as seen in the Figure, and whose sides are 1 foot in length. Suppose also that there’s a quarter circle inscribed in the square dartboard. The radius of the circle is 1 foot, and its area is π/4 square feet. If the points that are hit by the darts are uniformly distributed (and we always hit the square), then the number of darts that hit inside the circle should approximately satisfy the equation:

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