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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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