The path C is a line segment of length 5 in the plane starting at (4, 1). For f(x, y) = 4x + 3y, considerVƒ•dř.(a) Where should the other end of the line segment C be placed to maximize the value of the integral?At x =· y =(b) What is the maximum value of the integral?maximum value = IFor each of the following vector fields F, decide whether it is conservative or not by computing the appropriate first order partial derivatives.Type in a potential function f (that is, Vf = F) with f(0, 0) = 0. If it is not conservative, type N.А. F (х, у) — (6х + у)і + (х + 4у)jf (x, y) =В. F (х, у) — Зуi + 4xjf (x, y) =C. F (x, y) = (3 sin y) i+ (2y + 3x cos y)jf (х, у) —Note: Your answers should be either expressions of x and y (e.g. "3xy + 2y"), or the letter "N"

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Answered: The path C is a line segment of length…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 25E

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The path C is a line segment of length 5 in the plane starting at (4, 1). For f(x, y) = 4x + 3y, consider Vf• dr. (a) Where should the other end of the line segment C be placed to maximize the value of the integral? At x = , y = (b) What is the maximum value of the integral? maximum value =