We consider f: R → R by f(x) = x²-3x. From Calculus, it is known that of (a) = 2x-3. We'll compute forward difference approximations and symmetric difference approximations at xo = 1, for three values of h> 0. While it would be good to try another value of co, we don't have the heart to make you do that many hand computations! (a) Using the formulas in the notes, show all of the calculations to determine the first row of Table 2. By all calculations, it is meant, show the values for f(xo + h), (f(xo+h)-f(xo)), etc. as you arrive at your numerical approximations of the derivative. (b) Complete the table without showing any further calculations

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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dx
3. We consider f: R → R by f(x) = x² – 3x. From Calculus, it is known that f(x) = 2x-3. We'll compute forward difference
approximations and symmetric difference approximations at xo = 1, for three values of h> 0. While it would be good to try
another value of xo, we don't have the heart to make you do that many hand computations!
(a) Using the formulas in the notes, show all of the calculations to determine the first row of Table 2. By all calculations,
it is meant, show the values for f(xo+h), (f(xo+h)-f(xo)), etc. as you arrive at your numerical approximations of
the derivative.
(b) Complete the table without showing any further calculations
Table 2: My Table Comparing Numerical Derivatives to the Real Thing.
df (x)
dx
|x=1
1
-1.00
-1.00
-1.00
h forward difference symmetric difference
0.001
0.01
0.1
Transcribed Image Text:dx 3. We consider f: R → R by f(x) = x² – 3x. From Calculus, it is known that f(x) = 2x-3. We'll compute forward difference approximations and symmetric difference approximations at xo = 1, for three values of h> 0. While it would be good to try another value of xo, we don't have the heart to make you do that many hand computations! (a) Using the formulas in the notes, show all of the calculations to determine the first row of Table 2. By all calculations, it is meant, show the values for f(xo+h), (f(xo+h)-f(xo)), etc. as you arrive at your numerical approximations of the derivative. (b) Complete the table without showing any further calculations Table 2: My Table Comparing Numerical Derivatives to the Real Thing. df (x) dx |x=1 1 -1.00 -1.00 -1.00 h forward difference symmetric difference 0.001 0.01 0.1
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