Numerical Analysis
10th Edition
ISBN: 9781305253667
Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden
Publisher: Cengage Learning
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Chapter 3.4, Problem 1DQ
To determine
The polynomial that matches the function and the derivative.
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3. [1.14/4 Points]
DETAILS
MY NOTES
LARLINALG8 6.4.013.
Let B = {(1, 3), (-2, -2)} and B' = {(−12, 0), (-4, 4)} be bases for R², and let
42
- [13]
A =
30
be the matrix for T: R² R² relative to B.
(a) Find the transition matrix P from B' to B.
6
4
P =
9
4
(b) Use the matrices P and A to find [v] B and [T(V)] B, where
[v]B[31].
26
[V] B =
->
65
234
[T(V)]B=
->
274
(c) Find P-1 and A' (the matrix for T relative to B').
-1/3
1/3
-
p-1 =
->
3/4
-1/2
↓ ↑
-1
-1.3
A' =
12
8
↓ ↑
(d) Find [T(v)] B' two ways.
4.33
[T(v)]BP-1[T(v)]B =
52
4.33
[T(v)]B' A'[V]B' =
52
目
67%
PREVIOUS ANSWERS
ill
ASK YOUR TEACHER
PRACTICE ANOTHER
The function f is given by
f(x) = cos(x + 1). The solutions to which
6
of the following equations on the interval
0≤ x ≤ 2 are the solutions to f(x) = 1½
on the interval 0 < x < 2π?
2
A
√√3 cos x - sin x
= 1
B
√√3 cos x + sin x = 1
C
√3 sin x
COS x = 1
D
√√3 sin x + cos x = 1
Suppose that the graph below is the graph of f'(x), the derivative of f(x).
Find the locations of all relative extrema, and tell whether each extremum is
a relative maximum or minimum.
Af'(x)
Select the correct choice below and fill in the answer box(es) within
your choice.
(Simplify your answer. Use a comma to separate answers
as needed.)
-10 86-4-2
-9-
B
10
X
G
A. The function f(x) has a relative maximum at x=
relative minimum at x =
and a
B. The function f(x) has a relative maximum at x=
no relative minimum.
and has
C. There is not enough information given.
D. The function f(x) has a relative minimum at x=
no relative maximum.
and has
E. The function f(x) has no relative extrema.
Chapter 3 Solutions
Numerical Analysis
Ch. 3.1 - For the given functions f(x), let x0 = 0, x1 =...Ch. 3.1 - Use Theorem 3.3 to find an error bound for the...Ch. 3.1 - Prob. 4ESCh. 3.1 - The data for Exercise 6 were generated using the...Ch. 3.1 - Prob. 9ESCh. 3.1 - Prob. 10ESCh. 3.1 - Prob. 11ESCh. 3.1 - Prob. 12ESCh. 3.1 - Prob. 15ESCh. 3.1 - Prob. 17ES
Ch. 3.1 - It is suspected that the high amounts of tannin in...Ch. 3.1 - Prob. 21ESCh. 3.1 - Prove Taylors Theorem 1.14 by following the...Ch. 3.1 - Prob. 1DQCh. 3.1 - If we decide to increase the degree of the...Ch. 3.2 - Let P3(x) be the interpolating polynomial for the...Ch. 3.2 - Nevilles method is used to approximate f(0.4),...Ch. 3.2 - Nevilles method is used to approximate f(0.5),...Ch. 3.2 - Suppose xj = j, for j = 0, 1, 2, 3, and it is...Ch. 3.2 - Nevilles Algorithm is used to approximate f(0)...Ch. 3.2 - Prob. 11ESCh. 3.2 - Prob. 13ESCh. 3.2 - Can Nevilles method be used to obtain the...Ch. 3.3 - Use Eq. (3.10) or Algorithm 3.2 to construct...Ch. 3.3 - Use Eq. (3.10) or Algorithm 3.2 to construct...Ch. 3.3 - Use the Newton forward-difference formula to...Ch. 3.3 - Use the Newton forward-difference formula to...Ch. 3.3 - Use the Newton backward-difference formula to...Ch. 3.3 - Use the Newton backward-difference formula to...Ch. 3.3 - a. Use Algorithm 3.2 to construct the...Ch. 3.3 - a. Use Algorithm 3.2 to construct the...Ch. 3.3 - a. Approximate f(0.05) using the following data...Ch. 3.3 - The following data are given for a polynomial P(x)...Ch. 3.3 - The following data are given for a polynomial P(x)...Ch. 3.3 - The Newton forward-difference formula is used to...Ch. 3.3 - Prob. 14ESCh. 3.3 - Prob. 16ESCh. 3.3 - Prob. 17ESCh. 3.3 - Show that the polynomial interpolating the...Ch. 3.3 - Prob. 20ESCh. 3.3 - Prob. 21ESCh. 3.3 - Prob. 22ESCh. 3.3 - Prob. 23ESCh. 3.3 - Compare and contrast the various...Ch. 3.3 - Is it easier to add a new data pair using...Ch. 3.3 - Prob. 3DQCh. 3.4 - Use Theorem 3.9 or Algorithm 3.3 to construct an...Ch. 3.4 - Use Theorem 3.9 or Algorithm 3.3 to construct an...Ch. 3.4 - The data in Exercise 1 were generated using the...Ch. 3.4 - The data in Exercise 2 were generated using the...Ch. 3.4 - Let f (x) = 3xex e2x. a. Approximate f (1.03) by...Ch. 3.4 - The following table lists data for the function...Ch. 3.4 - a. Show that H2n + 1 (x) is the unique polynomial...Ch. 3.4 - Prob. 1DQCh. 3.4 - Prob. 2DQCh. 3.4 - Prob. 3DQCh. 3.5 - Determine the natural cubic spline S that...Ch. 3.5 - Determine the clamped cubic spline s that...Ch. 3.5 - Construct the natural cubic spline for the...Ch. 3.5 - Construct the natural cubic spline for the...Ch. 3.5 - The data in Exercise 3 were generated using the...Ch. 3.5 - Prob. 6ESCh. 3.5 - Prob. 8ESCh. 3.5 - Prob. 11ESCh. 3.5 - Prob. 12ESCh. 3.5 - Prob. 13ESCh. 3.5 - Prob. 14ESCh. 3.5 - Given the partition x0 = 0, x1 = 0.05, and x2 =...Ch. 3.5 - Prob. 16ESCh. 3.5 - Prob. 21ESCh. 3.5 - Prob. 22ESCh. 3.5 - Prob. 23ESCh. 3.5 - It is suspected that the high amounts of tannin in...Ch. 3.5 - Prob. 29ESCh. 3.5 - Prob. 30ESCh. 3.5 - Prob. 31ESCh. 3.5 - Prob. 32ESCh. 3.5 - Let f C2[a, b] and let the nodes a = x0 x1 xn...Ch. 3.5 - Prob. 34ESCh. 3.5 - Prob. 35ESCh. 3.6 - Let (x0, y0) = (0,0) and (x1, y1) = (5, 2) be the...Ch. 3.6 - Prob. 2ESCh. 3.6 - Prob. 5ESCh. 3.6 - Prob. 1DQ
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