Below is a function . 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 as a function of both its input variables and its parameters, using the notation f(x, y; a, b, c). The “gradient of towards ”, denoted as ∇v f, is the vector of all partial derivatives of to the variables/parameters listed in v. Fill in the boxes.f(x, y; a, b, c) = a exp(2x) + by2 + cxy∇x,y f(x, y; a, b, c) = ?∇a,b,c f(x, y; a, b, c) =• If are very small real numbers, what is f(1,2; 3,4 + δ,5 + ε) − f(1,2; 3,4,5) approximately? Explain how you obtained the answer. Question 3Below is a functionf. We are interested in how changes in the values of the input variables x, y orparameters a, b, c affect f. To that aim, we write f as a function of both its input variables and itsparameters, using the notation f(x, y; a, b, c). The "gradient of f towards v", denoted as V, f, isthe 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 + cxyVryf(x, y; a, b, c) =x.yVabef(x, y; a, b, c) =• If ő, e are very small real numbers, what is f(1,2; 3,4 + 6,5 + e) -(1.2; 3,4,5)approximately? Explain how you obtained the answer.Answer:Explanation:

Given that fx,y;a,b,c=ae2x+by2+cxy

Answered: Below is a function . We are interested…

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 . 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 as a function of both its input variables and its parameters, using the notation f(x, y; a, b, c). The “gradient of towards ”, denoted as ∇v f, is the vector of all partial derivatives of to the variables/parameters listed in v. Fill in the boxes.
f(x, y; a, b, c) = a exp(2x) + by2 + cxy
∇x,y f(x, y; a, b, c) = ?
∇a,b,c f(x, y; a, b, c) =
• If are very small real numbers, what is f(1,2; 3,4 + δ,5 + ε) − f(1,2; 3,4,5) approximately? Explain how you obtained the answer.