Homework Answers
Problem 5. Let F(r,y) (e-v-v sinzy) ?-(ze-s + z sin zyj (1) Show that F is...
Problem 5. Let F(r,y) (e-v-v sinzy) ?-(ze-s + z sin zyj (1) Show that F is a gradient field. (2) Find a potential function f for it (3) Use the potential function f to evaluate F-ds, where x is the path x(t) = (t,t2) for 0sts1. (NO credit for any other method.)
8Two vector fields are given: F(x,y,z) - (esin(yz), ze* cos(yz), ye* cos(yz)) and F(x,y,z) = (z...
8Two vector fields are given: F(x,y,z) - (esin(yz), ze* cos(yz), ye* cos(yz)) and F(x,y,z) = (z cos y, xz sin y, x cos y). a) Determine which vector field above is conservative. Justify. Foly = fjol so, <ea sin(J2), 20% cos(82), y acos (92)) Conservative. b) For the vector field that is conservative, find a function f such that F - Vf. Lxelsing2, zetos yea, yet cosy 2 c) Use the Fundamental Theorem of Line Integrals to find the work...
Numbers 1 and 2 please • Giren f(x, y, z) = ye" + x1nz Find E,...
Numbers 1 and 2 please
• Giren f(x, y, z) = ye" + x1nz Find E, ly, la, tra, Exy 2 Given w= xy + y +XZ. X= s. cost y=s. sint z =t Find dw and dw dt
Problem 9. (20 points) Let F be the vector field F(x, y, z) = (ey, xey...
Problem 9. (20 points) Let F be the vector field F(x, y, z) = (ey, xey + e*, ye*). (a) (5 points) Compute V F(x, y, z). (b) (10 points) Find a potential function for F or explain why none exists. (c) (5 points) Find ScF. dr, where C is the curve consisting of the line segments from (0,0,0) to (1,2,0), from (1,2,0) to (1,2, 1), and from (1, 2, 1) to (1,2,2).
2 Suppose Vf(x, y, z) - 2xyze i ze* j + ye k. If f(0, 0,...
2 Suppose Vf(x, y, z) - 2xyze i ze* j + ye k. If f(0, 0, 0) 1, find f(2, 2, 3).
Et F(r, v) (3z2e* + sec z tan z,ze - 90y*). (a) Show that F is a conservative. (b) Find a functio...
et F(r, v) (3z2e* + sec z tan z,ze - 90y*). (a) Show that F is a conservative. (b) Find a function f (potential function) show that F Vf. (c) Use above result to evaluate JeFdr, where C is a smooth curve that begin at the point (2, 1) and ends at (0, 3). (cost, sint) from -2 to t = 줄 particle that moves along the curve. (Write the value of work done without evaluating d) Find the work...
4. Consider the system of equations rey - ye?w = 1 +vw and usin(EU) = w...
4. Consider the system of equations rey - ye?w = 1 +vw and usin(EU) = w sin(yw). du Using the implicit function theorem, show that (x, y) can be expressed as a differ- entiable function of (vw) near (v, w) = (0,1). Find the values of (u, w) = (0,1). Be sure to show work. and
Problem 4 lly is flying around a room; his position at time t is r(t) =...
Problem 4 lly is flying around a room; his position at time t is r(t) = (3.cost, 2 sint,t"). temperature in the room is given by the function f(x,y,z) 5+ y + x2 + ys. What is the rate of change of the temperature experienced by the fly at timet? Problem 5 Find and using the chain rule. 1. S(x,y) = ye*, 1 = vº +v and y = uv. 2. /(x, y, z) = xy +sin , x =...
Differentiate the function f(x) = $* V t2 + +5 dt Find the definite integral (4...
Differentiate the function f(x) = $* V t2 + +5 dt Find the definite integral (4 sint – 2 cos t)dt Find the indefinite integral. / (tan an x – 3)' sec? x dx
I need help with number 5 *C) For all X, YE A, LPJ = LYJ XEY...
I need help with number 5
*C) For all X, YE A, LPJ = LYJ XEY 5. Prove (b) of Theorem 3: If P is a partition of a set A, then A/(A/P) = P. 6. Prove that if E, and E, are both equivalence relations on a set A, then E, E2 - Thian A waleted the
Problem 5. Let F(r,y) (e-v-v sinzy) ?-(ze-s + z sin zyj (1) Show that F is a gradient field. (2) Find a potential function f for it (3) Use the potential function f to evaluate F-ds, where x is the path x(t) = (t,t2) for 0sts1. (NO credit for any other method.)
8Two vector fields are given: F(x,y,z) - (esin(yz), ze* cos(yz), ye* cos(yz)) and F(x,y,z) = (z cos y, xz sin y, x cos y). a) Determine which vector field above is conservative. Justify. Foly = fjol so, <ea sin(J2), 20% cos(82), y acos (92)) Conservative. b) For the vector field that is conservative, find a function f such that F - Vf. Lxelsing2, zetos yea, yet cosy 2 c) Use the Fundamental Theorem of Line Integrals to find the work...
Numbers 1 and 2 please
• Giren f(x, y, z) = ye" + x1nz Find E, ly, la, tra, Exy 2 Given w= xy + y +XZ. X= s. cost y=s. sint z =t Find dw and dw dt
Problem 9. (20 points) Let F be the vector field F(x, y, z) = (ey, xey + e*, ye*). (a) (5 points) Compute V F(x, y, z). (b) (10 points) Find a potential function for F or explain why none exists. (c) (5 points) Find ScF. dr, where C is the curve consisting of the line segments from (0,0,0) to (1,2,0), from (1,2,0) to (1,2, 1), and from (1, 2, 1) to (1,2,2).
2 Suppose Vf(x, y, z) - 2xyze i ze* j + ye k. If f(0, 0, 0) 1, find f(2, 2, 3).
et F(r, v) (3z2e* + sec z tan z,ze - 90y*). (a) Show that F is a conservative. (b) Find a function f (potential function) show that F Vf. (c) Use above result to evaluate JeFdr, where C is a smooth curve that begin at the point (2, 1) and ends at (0, 3). (cost, sint) from -2 to t = 줄 particle that moves along the curve. (Write the value of work done without evaluating d) Find the work...
4. Consider the system of equations rey - ye?w = 1 +vw and usin(EU) = w sin(yw). du Using the implicit function theorem, show that (x, y) can be expressed as a differ- entiable function of (vw) near (v, w) = (0,1). Find the values of (u, w) = (0,1). Be sure to show work. and
Problem 4 lly is flying around a room; his position at time t is r(t) = (3.cost, 2 sint,t"). temperature in the room is given by the function f(x,y,z) 5+ y + x2 + ys. What is the rate of change of the temperature experienced by the fly at timet? Problem 5 Find and using the chain rule. 1. S(x,y) = ye*, 1 = vº +v and y = uv. 2. /(x, y, z) = xy +sin , x =...
Differentiate the function f(x) = $* V t2 + +5 dt Find the definite integral (4 sint – 2 cos t)dt Find the indefinite integral. / (tan an x – 3)' sec? x dx
I need help with number 5
*C) For all X, YE A, LPJ = LYJ XEY 5. Prove (b) of Theorem 3: If P is a partition of a set A, then A/(A/P) = P. 6. Prove that if E, and E, are both equivalence relations on a set A, then E, E2 - Thian A waleted the
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