Homework Answers
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the...
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
6 (20 pts). Let F(x, y, z) = x2 + y2 + x2 - 6xyz. (1)...
6 (20 pts). Let F(x, y, z) = x2 + y2 + x2 - 6xyz. (1) Find the gradient vector of F(x, y, z); (2) Find the tangent plane of the level surface F(x, y, z) = x2 + y2 + x2 - 6xyz = 4 at (0, 0, 2); (3) The level surface F(x, y, z) = 4 defines a function z = f(x,y). Use linear approxi- mation to approximate z = = f(-0.002,0.003).
1. Suppose F = (-y,x,z) and S is the part of the sphere x2 + y2...
1. Suppose F = (-y,x,z) and S is the part of the sphere x2 + y2 + z = 25 below the plane z = 4, oriented with the outward-pointing normal (so that the normal at (5,0,0) is 1). Compute the flux integral curl F.ds using Stoke's theorem.
1. Consider lim (z,y)=(0,0) 2 + y2 Compute the limit along the two lines y =...
1. Consider lim (z,y)=(0,0) 2 + y2 Compute the limit along the two lines y = 0 and yma. 2. Let F(x,y) = sin(x”y), where = sin(u) + cos(u) and y = ew. Use the chain rule (substitution will earn zero credit) to find 3. Find the maximum rate of change of f(x,y) - eat (1,1) and the direction in which it occurs.
4. Let f(x, y, z) = rytan'() + z sin(xy), < = wy=v²v, z = "....
4. Let f(x, y, z) = rytan'() + z sin(xy), < = wy=v²v, z = ". Find fu and , using the chain rule.
Please help me solve this problem. Thanks! Problem 1 (weight 25%) Consider the problem Maximise f(x, y, z) = x + y +2z when g(x,y,z) = x2 +y2 +2z2 = 4. (*) (a) Explain why the problem (*) does have a...
Please help me solve this problem.
Thanks!
Problem 1 (weight 25%) Consider the problem Maximise f(x, y, z) = x + y +2z when g(x,y,z) = x2 +y2 +2z2 = 4. (*) (a) Explain why the problem (*) does have a solution (b) Suppose that ( has a solution, and use Lagrange's method to set up the necessary conditions for solving the problem. (c)Find all the triplets (r. y, 2) that satisfy the necessary conditions for solving the problem (*),...
(1 point) Suppose F(x, y, z) = (x, y, 4z). Let W be the solid bounded...
(1 point) Suppose F(x, y, z) = (x, y, 4z). Let W be the solid bounded by the paraboloid z = x2 + y2 and the plane z = 4. Let S be the closed boundary of W oriented outward. (a) Use the divergence theorem to find the flux of F through S. ſ FdA = 48pi S (b) Find the flux of F out the bottom of S (the truncated paraboloid) and the top of S (the disk). Flux...
please help with these questions 7. Find fryzx, for f(x, y, z) = 3 + 2?x...
please help with these questions
7. Find fryzx, for f(x, y, z) = 3 + 2?x – xyz + x+y 8. Use the chain rule to calculate that t = 0, if z = sin(xy), x = 1+1, y = 12 + 2t. 9. Use the chain rule to find us at (u, v) = (1,0), when z = xy, x = u +v?, y = x + v.
where g is a function of one variable 16. Suppose that f(x,y,z)= g(V x2 + y2...
where g is a function of one variable 16. Suppose that f(x,y,z)= g(V x2 + y2 + such that g(3) = 4. Evaluate ſyf(x,y,z)ds' where S is the sphere x² + y2 +z2 =9.
Evaluatef(x, y, z) dS. f(x, y, z) = x2 + y2 +z2
Evaluatef(x, y, z) dS. f(x, y, z) = x2 + y2 +z2
Evaluatef(x, y, z) dS. f(x, y, z) = x2 + y2 +z2
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
6 (20 pts). Let F(x, y, z) = x2 + y2 + x2 - 6xyz. (1) Find the gradient vector of F(x, y, z); (2) Find the tangent plane of the level surface F(x, y, z) = x2 + y2 + x2 - 6xyz = 4 at (0, 0, 2); (3) The level surface F(x, y, z) = 4 defines a function z = f(x,y). Use linear approxi- mation to approximate z = = f(-0.002,0.003).
1. Suppose F = (-y,x,z) and S is the part of the sphere x2 + y2 + z = 25 below the plane z = 4, oriented with the outward-pointing normal (so that the normal at (5,0,0) is 1). Compute the flux integral curl F.ds using Stoke's theorem.
1. Consider lim (z,y)=(0,0) 2 + y2 Compute the limit along the two lines y = 0 and yma. 2. Let F(x,y) = sin(x”y), where = sin(u) + cos(u) and y = ew. Use the chain rule (substitution will earn zero credit) to find 3. Find the maximum rate of change of f(x,y) - eat (1,1) and the direction in which it occurs.
4. Let f(x, y, z) = rytan'() + z sin(xy), < = wy=v²v, z = ". Find fu and , using the chain rule.
Please help me solve this problem.
Thanks!
Problem 1 (weight 25%) Consider the problem Maximise f(x, y, z) = x + y +2z when g(x,y,z) = x2 +y2 +2z2 = 4. (*) (a) Explain why the problem (*) does have a solution (b) Suppose that ( has a solution, and use Lagrange's method to set up the necessary conditions for solving the problem. (c)Find all the triplets (r. y, 2) that satisfy the necessary conditions for solving the problem (*),...
(1 point) Suppose F(x, y, z) = (x, y, 4z). Let W be the solid bounded by the paraboloid z = x2 + y2 and the plane z = 4. Let S be the closed boundary of W oriented outward. (a) Use the divergence theorem to find the flux of F through S. ſ FdA = 48pi S (b) Find the flux of F out the bottom of S (the truncated paraboloid) and the top of S (the disk). Flux...
please help with these questions
7. Find fryzx, for f(x, y, z) = 3 + 2?x – xyz + x+y 8. Use the chain rule to calculate that t = 0, if z = sin(xy), x = 1+1, y = 12 + 2t. 9. Use the chain rule to find us at (u, v) = (1,0), when z = xy, x = u +v?, y = x + v.
where g is a function of one variable 16. Suppose that f(x,y,z)= g(V x2 + y2 + such that g(3) = 4. Evaluate ſyf(x,y,z)ds' where S is the sphere x² + y2 +z2 =9.
Evaluatef(x, y, z) dS. f(x, y, z) = x2 + y2 +z2
Evaluatef(x, y, z) dS. f(x, y, z) = x2 + y2 +z2
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