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.
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.
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
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.
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