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MATLAB - David Thibodeaux Math 111 H03 Matlab assignment#1...

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David Thibodeaux Math 111 – H03 Matlab assignment #1 In this assignment, we will compare two different methods used to find the limit of f(x) as x approaches c, and determine which method is preferable. The first method plots a secant line using f(c) and f(c+h), with the values of h = .5, 1, and 2. The second method uses the points f(c+h) and f(c-h), with the same values for h. Part 1: The first equation we will use in this assignment is f(x) = x 3 After running the script in MATLAB, the following graphs were produced: Figure 1.1 (Using f(1), f(1+h))
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Figure 1.2 (Using f(1-h), f(1+h)) Tables Describing numerical results: First Method Second Method h Slope h Slope 2 13.00000 2 7.0000000 1 7.000000 1 4.0000000 .5 4.750000 .5 3.2500000 0 3.000000 0 3.0000000 Analysis: Upon observing the differing methods to determine the limit as x approaches 1, the method used in Fig. 1 seems more appropriate at first. Conceptually, it would seem that since the interval between f(1) and f(1+h) is less than f(1-h) and f(1+h), that the slope would be more accurate. However, upon analyzing the returned values, the second approach is mathematically more accurate, returning a slope of 3.25 at f(.5,1.5), while the
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