What is the curl of the vector fieldF(z, y, z) = ryi+ zyzj + yzkO a. (-ry+ z)i+ (yz – x)kO b. (Ty 2)i +(-yz+ x)jO c. (-ry + z)j + (yz - x)kO d. (zy- z)j +(-y2 + r)k

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Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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For the vector field (x³z², 0, -x²z), evaluate the line integral on the clase curve made by a square in the (x, 2) plane with corners at (1,0,1), (-1,01), (-1,0, -1), (1, 0,-1) in the counter clockwise direction.
ه پرس (2) Find the work of the force F = 3i + 2j - 4k, displaces an object from P(1,-1,2) to Q(2,-1,3). 0² (19-211) -> d=1-20 +1.K. +4j+ kW = ( 31+ 20-ak) (1.-2jHK)
4) Let V be the vector space of polynomials of degree <2 and let p(x) = ax² + bx + c. Find the adjoint operator (T*@)(p) for T:V → V and o:V → R given by d) Tp(x) = x²p(x) + x³p'(x), @(p) = p"(1).
1) F=Cy+2xz)i+ (x+ z²+1)j +(2yz+x)K Give the Vector field. Protected, ☆Fis the vector fied protected! Your show. If find a Potential function for the vector field "F".
3) Compute the curl of F= (4 xy) i + (2x² + 2z²) j + (4 yz) k.
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.
it says "Use symbolic notation and fractions where needed" and this is my only attempy
11.Vector analysis (calculus 4)
G is a vector field defined as G = Bxlnzi + Dy zj + (+ y³) k. b) If C is the straight line from (1,1,1) to (2,1,2) find S, 2xlnzdx + 2y²zdy +y dz.
What are V-F and VX F for the vector field F(x,y,z) = 3x²zi-ye*j - y²zk? OV.F = x²exy 2 VXF = x²i-3e²j+yk OF=3x²-xe* + 2yz VXF = 2i-3j-k V-F = 3x²-x-z VXF= -2yi+ 3xj + zk V-F = 6xz-e* - y² VXF = -2yzi + 3x²j-ye*k

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What is the curl of the vector field F(z, y, z) = ryi+ zyzj + yzk O a. (-ry + z)i + (yz – 2)k O b. (ry- z)i+(-yz + a)j O c.(-ry + z)j + (yz - x)k O d. (ry- 2)j +(-yz-+ x)k