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Below is a function f. We are interested in how changes in the values of the input variables x, y or parameters a, b, c affect f. To that aim, we write f as a function of both its input variables and its parameters, using the notation f(x, y; a, b, c). The "gradient of f towards v", denoted as V,f, is the vector of all partial derivatives of f to the variables/parameters listed in v. Fill in the boxes. fx, y; а, b, c) %3 а еxp(2x) + by? + сху • Vyf(x, y; a, b, c) = x,y. Vabof(x, y; a, b, c) = If 8, e are very small real numbers, what is f(1,2; 3,4 + 8,5 + e) – f(1,2; 3,4,5) approximately? Explain how you obtained the answer. Answer: Explanation:

Below is a function f. We are interested in how changes in the values of the input variables x, y or parameters a, b, c affect f. To that aim, we write f as a function of both its input variables and its parameters, using the notation f(x, y; a, b, c). The "gradient of f towards v", denoted as V,f, is the vector of all partial derivatives of f to the variables/parameters listed in v. Fill in the boxes. fx, y; а, b, c) %3 а еxp(2x) + by? + сху • Vyf(x, y; a, b, c) = x,y. Vabof(x, y; a, b, c) = If 8, e are very small real numbers, what is f(1,2; 3,4 + 8,5 + e) – f(1,2; 3,4,5) approximately? Explain how you obtained the answer. Answer: Explanation:

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Below is a function f. We are interested in how changes in the values of the input variables x, y or parameters a, b, c affect f. To that aim, we writef as a function of both its input variables and its parameters, using the notation f(x, y; a, b, c). The “gradient of f towards v", denoted as Vyf, is the vector of all partial derivatives of f to the variables/parameters listed in v. Fill in the boxes. • f(x, y; a, b, c) = a exp(2x) + by² + cxy • Vxyf(x, y; a, b, c) = Vabef(x, y; a, b, c) = • If ô, ɛ are very small real numbers, what is f(1,2; 3,4+ 8,5 + e) – f(1,2; 3,4,5) approximately? Explain how you obtained the answer. Answer: Explanation:
Transcribed Image Text:Below is a function f. We are interested in how changes in the values of the input variables x, y or parameters a, b, c affect f. To that aim, we writef as a function of both its input variables and its parameters, using the notation f(x, y; a, b, c). The “gradient of f towards v", denoted as Vyf, is the vector of all partial derivatives of f to the variables/parameters listed in v. Fill in the boxes. • f(x, y; a, b, c) = a exp(2x) + by² + cxy • Vxyf(x, y; a, b, c) = Vabef(x, y; a, b, c) = • If ô, ɛ are very small real numbers, what is f(1,2; 3,4+ 8,5 + e) – f(1,2; 3,4,5) approximately? Explain how you obtained the answer. Answer: Explanation:
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