Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
14th Edition
ISBN: 9780134668574
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker
Publisher: PEARSON
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Chapter B.4, Problem 11E
To determine
Whether a table with three points have linear, quadratic and cubic interpolating polynomial or not.
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Total marks 15
3.
(i)
Let FRN Rm be a mapping and x = RN is a given
point. Which of the following statements are true? Construct counterex-
amples for any that are false.
(a)
If F is continuous at x then F is differentiable at x.
(b)
If F is differentiable at x then F is continuous at x.
If F is differentiable at x then F has all 1st order partial
(c)
derivatives at x.
(d) If all 1st order partial derivatives of F exist and are con-
tinuous on RN then F is differentiable at x.
[5 Marks]
(ii) Let mappings
F= (F1, F2) R³ → R² and
G=(G1, G2) R² → R²
:
be defined by
F₁ (x1, x2, x3) = x1 + x²,
G1(1, 2) = 31,
F2(x1, x2, x3) = x² + x3,
G2(1, 2)=sin(1+ y2).
By using the chain rule, calculate the Jacobian matrix of the mapping
GoF R3 R²,
i.e., JGoF(x1, x2, x3). What is JGOF(0, 0, 0)?
(iii)
[7 Marks]
Give reasons why the mapping Go F is differentiable at
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[3 Marks]
Chapter B.4 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Ch. B.4 - Consider the points in Table 1. (A)Let...Ch. B.4 - Given the following polynomial and table,...Ch. B.4 - Prob. 1MPCh. B.4 - Prob. 2MPCh. B.4 - Prob. 3MPCh. B.4 - Prob. 4MPCh. B.4 - Prob. 1ECh. B.4 - Prob. 2ECh. B.4 - Prob. 3ECh. B.4 - Prob. 4E
Ch. B.4 - Prob. 5ECh. B.4 - Prob. 6ECh. B.4 - Prob. 7ECh. B.4 - Prob. 8ECh. B.4 - Prob. 9ECh. B.4 - Prob. 10ECh. B.4 - Prob. 11ECh. B.4 - Prob. 12ECh. B.4 - Prob. 13ECh. B.4 - In Problems 1320, use the interpolating polynomial...Ch. B.4 - Prob. 15ECh. B.4 - Prob. 16ECh. B.4 - Prob. 17ECh. B.4 - Prob. 18ECh. B.4 - Prob. 19ECh. B.4 - Prob. 20ECh. B.4 - Prob. 21ECh. B.4 - Prob. 22ECh. B.4 - In Problems 2130, find the interpolating...Ch. B.4 - Prob. 24ECh. B.4 - Prob. 25ECh. B.4 - Prob. 26ECh. B.4 - Prob. 27ECh. B.4 - Prob. 28ECh. B.4 - Prob. 29ECh. B.4 - Prob. 30ECh. B.4 - Prob. 31ECh. B.4 - Prob. 32ECh. B.4 - Prob. 33ECh. B.4 - Prob. 34ECh. B.4 - The following table was obtained from the function...Ch. B.4 - Prob. 36ECh. B.4 - Prob. 37ECh. B.4 - The following table was obtained from the function...Ch. B.4 - Prob. 39ECh. B.4 - Prob. 40ECh. B.4 - Prob. 41ECh. B.4 - Prob. 42ECh. B.4 - Prob. 43ECh. B.4 - Prob. 44ECh. B.4 - Maximum revenue. The revenue R (in thousands of...Ch. B.4 - Minimum overage cost. The cost C (in thousands of...Ch. B.4 - Prob. 47ECh. B.4 - Prob. 48ECh. B.4 - Prob. 49ECh. B.4 - Prob. 50ECh. B.4 - Voter registration. The number N of registered...Ch. B.4 - Voter registration. The number N of registered...
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