(1 point) Let R be the rectangle with vertices (0,0). (8,0). (8, 8), and (0,8) and let f(x, y)- /...
Let F(x, y) = ( – 7x, 5y) and let R be the rectangle with vertices (0,0), (5,0), (0,3), and (5,3). Compute the flux of F across the rectangle. Begin by parameterizing each side of rectangle (oriented counterclockwise), and then compute the flux integral over each side individually. Preview
Values of f (x, y are in the table below. 68 10 у0.2 5 719 4 6 5 Let R be the rectangle: 4.0 Sx 4.2 0.0 S y 0.4. Based on the values given in the table, find Riemann sums which are reasonable over and underestimates for f x, y) dA with ΔΧ-0.1 and Δy 0.2. Enter the exact answers. Lower sum Upper sum Values of f (x, y are in the table below. 68 10 у0.2 5 719...
2. (1 Point) Let r-2u and y-3u. (a) Let R be the rectangle in the uv-plane defined by the points (0,0), (2,0), (2,1), (0 , 1). Find the area of the image of R in the ry plane? (b) Find the area of R by computing the Jacobian of the transformation from uv-space to xy-space Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice...
Find the average value of f over the given rectangle. f(x,y) =4x2y, R has vertices (-2,0),(-2,5),(2,5),(2,0).
12. Let R ((x, y)l0 s r s 4,0 s y s 6). Let f(x, y)2+2y Express the Riemann sum estimate for Jjf(x, y)dA with m 2,n 3 using both summation notation and expanded sum form if the sample points are the upper right corners of each sub-rectangle. Do not evaluate. 12. Let R ((x, y)l0 s r s 4,0 s y s 6). Let f(x, y)2+2y Express the Riemann sum estimate for Jjf(x, y)dA with m 2,n 3 using...
(1 point) Let Vf =-8xe-r sin(5y) 20e-x. cos(Sy) j. Find the change inf between (0,0) and (1, π/2) in two ways vf . dr, where C is a curve connecting (0,0) and (1.d2). (a) First, find the change by computing the line integral The simplest curve is the line segment joining these points. Parameterize it: with 03t s 1, r(t)- so that Icvf . di- Note that this isn't a very pleasant integral to evaluate by hand (though we could...
(1 point) A uniform magnetic field B has constant strength b teslas in the 2-direction [ie., B = (0,0, b) ] (a) Verify that A Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A= (4,0,4), С=(0,3,0), В= (4,3,0), D (0,0, 4), F (4,0, 0) Flux(B) (1 point) A uniform magnetic field B has constant strength b...
(1 point) Find the average value of f(x,y) = 2x + ey over the rectangle R = [0,5] x [0,7]. Average value =
1. 2. (1 point) Let f(x,y,z) = 4x2 + xy + yz +5z?. Find the linearization L(x, y, z) of f(x,y,z) at the point (-1, -3, -1). L(x,y,z) = -5x-2y+72-3 Find an upper bound for the magnitude El of the error in the approximation f(x, y, z) ~ L(x, y, z) over the box |x +11 30.04, \y +31 < 0.04, 12 +11 30.04. E 3 (1 point) Let f(x, y) = 3 In(x) +2 In(y). Find the linearization L(av)...
q4 please thanks (1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...