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Example text
The following code calculates the Riemann sum and produces the graphical data. b,color=black): The plot structures vert0 and vertN contain the beginning and ending vertical line segments, which are not contained in the tread-riser plots constructed in the do loop. The name horiz contains the plot structure for the line segment [a, b]. 3Maple has a command for drawing all the rectangles that comprise the approximating area, but here we are concerned with writing our own code for a slightly di erent “gure.
Use a fine enough grid so that the curve appears smooth. In the same picture plot the circle x2 + y 2 = 1 and use the fsolve command to find all points of intersection of this circle with the assigned curve. Annotate your picture, identifying the respective curves. 5, use the fsolve command to find all solutions to H(1 + h, y) = 0. This will give one or more points (1 + h, y) on the curve. Plot the tangent lines at these points (with suitable length) and the curve itself (for x [0, 2]) in the same picture.
N). 001. For this example, checking the value of k will give k = 31. 001 of the true value S for the sum of the series. 4 illustrates these results and how they oscillate above and below the exact value S for the sum of the series. The calculations and the theory give us the following approximation of the value of S. 3877824043. One can show (exercise) that the exact value is S = 2 ln 2 − 1. You should bear in mind that the above code for the while loop assumes that the terms an in the series satisfy conditions (1) and (2) of the Alternating Series Test.