Numerical Analysis
10th Edition
ISBN: 9781305253667
Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden
Publisher: Cengage Learning
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Chapter 1.1, Problem 18ES
Let f(x) = (1 − x)−1 and x0 = 0. Find the nth Taylor polynomial Pn(x) for f(x) about x0. Find a value of n necessary for Pn(x) to approximate f(x) to within 10−6 on [0, 0.5].
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Chapter 1 Solutions
Numerical Analysis
Ch. 1.1 - Show that the following equations have at least...Ch. 1.1 - Show that the following equations have at least...Ch. 1.1 - Find intervals containing solutions to the...Ch. 1.1 - Find intervals containing solutions to the...Ch. 1.1 - Find maxaxb |f(x)| for the following functions and...Ch. 1.1 - Find maxaxb | f(x)| for the following functions...Ch. 1.1 - Show that f(x) is 0 at least once in the given...Ch. 1.1 - Suppose f C[a, b] and f (x) exists on (a, b)....Ch. 1.1 - Let f(x) = x3. a. Find the second Taylor...Ch. 1.1 - Find the third Taylor polynomial P3(x) for the...
Ch. 1.1 - Find the second Taylor polynomial P2(x) for the...Ch. 1.1 - Repeat Exercise 11 using x0 = /6. 11. Find the...Ch. 1.1 - Prob. 13ESCh. 1.1 - Prob. 14ESCh. 1.1 - Prob. 15ESCh. 1.1 - Use the error term of a Taylor polynomial to...Ch. 1.1 - Use a Taylor polynomial about /4 to approximate...Ch. 1.1 - Let f(x) = (1 x)1 and x0 = 0. Find the nth Taylor...Ch. 1.1 - Let f(x) = ex and x0 = 0. Find the nth Taylor...Ch. 1.1 - Prob. 20ESCh. 1.1 - The polynomial P2(x)=112x2 is to be used to...Ch. 1.1 - Use the Intermediate Value Theorem 1.11 and Rolles...Ch. 1.1 - Prob. 23ESCh. 1.1 - In your own words, describe the Lipschitz...Ch. 1.2 - Compute the absolute error and relative error in...Ch. 1.2 - Compute the absolute error and relative error in...Ch. 1.2 - Prob. 3ESCh. 1.2 - Find the largest interval in which p must lie to...Ch. 1.2 - Perform the following computations (i) exactly,...Ch. 1.2 - Use three-digit rounding arithmetic to perform the...Ch. 1.2 - Use three-digit rounding arithmetic to perform the...Ch. 1.2 - Repeat Exercise 7 using four-digit rounding...Ch. 1.2 - Repeat Exercise 7 using three-digit chopping...Ch. 1.2 - Prob. 10ESCh. 1.2 - Prob. 11ESCh. 1.2 - Prob. 12ESCh. 1.2 - Let f(x)=xcosxsinxxsinx. a. Find limx0 f(x). b....Ch. 1.2 - Let f(x)=exexx. a. Find limx0(ex ex )/x. b. Use...Ch. 1.2 - Use four-digit rounding arithmetic and the...Ch. 1.2 - Prob. 16ESCh. 1.2 - Prob. 17ESCh. 1.2 - Repeat Exercise 16 using four-digit chopping...Ch. 1.2 - Use the 64-bit-long real format to find the...Ch. 1.2 - Prob. 23ESCh. 1.2 - Discuss the difference between the arithmetic...Ch. 1.2 - Prob. 2DQCh. 1.2 - Discuss the various different ways to round...Ch. 1.2 - Discuss the difference between a number written in...Ch. 1.3 - The Maclaurin series for the arctangent function...Ch. 1.3 - Prob. 4ESCh. 1.3 - Prob. 5ESCh. 1.3 - Find the rates of convergence of the following...Ch. 1.3 - Find the rates of convergence of the following...Ch. 1.3 - Prob. 8ESCh. 1.3 - Prob. 9ESCh. 1.3 - Suppose that as x approaches zero,...Ch. 1.3 - Prob. 11ESCh. 1.3 - Prob. 12ESCh. 1.3 - Prob. 13ESCh. 1.3 - Prob. 14ESCh. 1.3 - a. How many multiplications and additions are...Ch. 1.3 - Write an algorithm to sum the finite series i=1nxi...Ch. 1.3 - Construct an algorithm that has as input an...Ch. 1.3 - Let P(x) = anxn + an1xn1 + + a1x + a0 be a...Ch. 1.3 - Prob. 4DQCh. 1.3 - Prob. 5DQCh. 1.3 - Prob. 6DQ
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