2. (Section 17.3) Given the vector field 7³ (2, y, z) — (In z + sex²(x + y))i + (x²(x + y) +5² +2²) ³+√² + 2²k,=(a) Show that is conservative.(b) Find the potential function f(x, y, z).(e) Find the work done by in moving a particle along a path from (1,0, 1) to (2,1,0).

Answered: Image /qna-images/answer/fb7a82a9-a955-4ae8-8635-a2fb67166cdc.jpg

Answered: 2. (Section 17.3) Given the vector…

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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1. (Section 17.1) Match the vector fields with their sketches below by placing the letter of the function in the corresponding blank: (I) F(x, y) = (II) F(x, y) = (III) F(x, y) = (IV) F(x, y) = Vector Field: (B) Vector Field: (A) (C) Vector Field (D) 0 Vector Field:
How large should n be to guarantee that the Trapezoidal Rule approximation to 14x – 60z? – læ + 3)dx is accurate to within 0.1. 5 n = How large should n be to guarantee that the Simpsons Rule approximation to | (-24 – 14x – 60z? – læ + 3)dx is accurate to within 0.1. n = Hint: Remember your answers should be a whole numbers, and Simpson's Rule requires even values for n
(1) Give an example of a function z = f(x, y) and a unit vector i such that f.(0,0) = 2, fy(0,0) = 1 and fã(0,0) is negative.
1. Consider two vector fields: F1(x, y) = -yi+ xj and F2(7) = F. (a) Evaluate F and F, at the given points. (x, y) (1,0) (0, 1) (-1,0) (0, –1) F(r, y) F(1, y) (т, у) (1,1) (-1,1) (-1,–1) (1, –1) F(1, y) F(x, y) On the grids shown below, sketch above vectors of vector fields F (b) and F. F;(x, y) = -yi + xj F2(F) = F.
I need help to directly evaluate S1 by using the vector fields formula as shown below in second picture.
3. (b) Let f(x, y) = log((ry - 2)²), u =(³, 4). i. Calculate the directional derivative Vaf (3, 1). ii. Determine the unit vector (direction) u for which Vaf (3, 1) is maximal.
2.2 please solve it on paper
9.Vector analysis (calculus 4)

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2. (Section 17.3) Given the vector field F(x, y, z) — (In z + sex²(x + y))i + (sex²(x+y)+ 7²+2) (a) Show that is conservative. (b) Find the potential function ƒ(z, y, z).