(3m/2.0,0) 4(n/2./2,0)(0.3x/2.0)2. Let F(x, y, z) = (3x²y - z sin(x))i + x³ + cos(x)k and let C be the piecewise smooth curvefrom (0, 37,0) to (0,0, 57) shown in the figure. Compute [F(r). dr. (976337703)

Answered: Image /qna-images/answer/249c715c-d0f9-4cd1-8078-69ea5a1b0bd0.jpg

Answered: (3m/2.0,0)4 (m/2. m/2,0) (0.3=/2.0) 2.…

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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Q1/ Prove that the value of |cos(-)dz, when C is the line segment from z = 0 to Z = T + 2i is e +e-1
Find the length of the curve r(t) = (4 cos(t) + 4t sin(t))i + (4 sin(t) - 4t cos(t))j + (3-√3²) K 2 a) ○ 344 π² √2 b) 6 π √43 c) ○ 2 π² √43 d) ○ 344 π √/2 e) ○ 47² √/43 k from t = 0 tot = 2.
Suppose Vf(x, y) = 3y sin(xy)i + 3x sin(xy)j, F = ▼ ƒ(x, y), and C is the segment of the parabola y = 2x² from the point (1, 2) to (5, 50). Then LE F·dr =
35. Evaluate F.dr: (a) F = (x+z)i +zj+yk. C is the line from (2,4,4) to (1,5,2). (b) F= x²i+zsin(yz)j + y sin(yz)k. C is the curve from A4(0,0,1) to B(3,1,2) as shown below. B A (c) F = yi-xj+zk. C is the circle of radius 3 centered on the z-axis in the plane z=4 oriented clockwise when viewed from above. (d) F = 4x³i + (x+y)j. C is the curve y=sin(2x) from (0,0) to (7/2,0). (e) F = (-y³ + sin(x²))ī + (x³ − ln(y² +1)) j . C is the circle of radius 5 centered at (0,0) in the .xy- plane oriented counterclockwise.
Q4. A point is moving along a curve that is given as: R(1) = (cos 31)i + (sin 31)j + (31)k. Find: a) The derivative of the function f(x, y, z)= xyz in the direction of the velocity vector of the given curve at t= π/3. b) How far does the point travel along its path from t=0 to t = 2.
11. C is the curve F(1) = ( In (2 – t),iVI+3 Find parametric equations for the tangent line to C at the point (0, 1, 2).
5. The function r(t) moving in 3D space. = (2 sin (¹), 3, 2 cos (t)) parametrizes (draws) the path of a particle (a) Evaluate r(t) at t = 0, 1, 2, 3, 4.

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(3m/2.0,0)4 (m/2. m/2,0) (0.3=/2.0) 2. Let F(x, y, z) = (3x²y - z sin(x))i + x³ + cos(x)k and let C be the piecewise smooth curve from (0, 37,0) to (0,0, 5) shown in the figure. Compute [ F(r) dr. (976337703)