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(ch), 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(1h), 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(1h) 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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 Spring '11
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 Calculus, Derivative, Slope, UCI race classifications, Tour de Georgia

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