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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Let A(t) = f(t)i + f₂(1) and B(t) = g₁(t)i + g₂(t)},t = [0, 1], where f₁f2, 81, 82 are continuous functions. If A(t) and B(t) are non-zero vectors for all and 7(0) = 2î +3ĵ, A(1) = 6î +2), B(0)=31 +23 and 6i- A B(1) = 27 +6, then show that A(1) and B(t) are parallel for some t.
Suppose f(x, y) = √/tan(x) + y and u is the unit vector in the direction of (1, 1). Then, (a) ▼ f(x, y) = (b) ▼ ƒ(−0.8, 10) = (c) fu (−0.8, 10) = Du f(−0.8, 10) =
(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.
Clear steps please!
How many terms of the series do we need to add in order to find the sum to the indicated accuracy?
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.
Which of the following vector fields are conservative? (i) F(x, y) = (10x²y⁹+6)i + (9x³y² + 8) j (ii) F(x, y) = (9ye³x + cos 6y)i + (e⁹x + 6x sin 6y) j (iii) F(x, y) = 10y²e10xy i+ (10+xy) e10xy j
2.2 please solve it on paper
Let A(t) = f(t)i + f₂(1) and B(t) = g₁(t)i + g₂(t)},t = [0, 1], where f₁f2, 81, 82 are continuous functions. If A(t) and B(t) are non-zero vectors for all and 7(0) = 2î +3ĵ, A(1) = 6î +2), B(0)=31 +23 and 6i- A B(1) = 27 +6, then show that A(1) and B(t) are parallel for some t.

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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).