Homework Answers
Consider F and C below. F(x, y, z) = yze?i + e'?j + xyek, C: r(t)...
Consider F and C below. F(x, y, z) = yze?i + e'?j + xyek, C: r(t) - (t? + 1)i + (t? - 1)j + (t– 3t)k, Osts3 (a) pind a function f such that F – Vf. f(x, y, z) (b) Use part (a) to evaluate F. dr along the given curve C.
Let f(x,y,z) = xy + z-5,x=r +2s, y = 2r - sec(s), z = s Then...
Let f(x,y,z) = xy + z-5,x=r +2s, y = 2r - sec(s), z = s Then I is: ar a. r - sec(s) b. sec(s) c. r+s+sec(s) d. 4r + 4s - sec(s) a. b. C. Given zº – xy + y2 + y2 = 2 and z is a differentiable function in x and y. Then at (1,1,1) is: дх a. 0 b. 1 c. d. e. None of the above o a. o b. ♡ C. o d.
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš...
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš sin () + yś sin () if xy + 0 242ADES if xy = 0 ii. Prove that every linear transformation T:R" - R" is continuous on R". iii. Let f:R" → R and a ER" Define Dis (a), the i-th partial derivative of f at a, 1 sisn. Determine whether the partial derivatives of f exist at (0,0) for the following function. In...
a(x,y,z) (1 point) Find the Jacobian. a(s,t,u) where x = 3t – 2s – 4u, y=...
a(x,y,z) (1 point) Find the Jacobian. a(s,t,u) where x = 3t – 2s – 4u, y= -(2s + 4t+2u), z = 4t – 2s + 5u. 9 a(z,y,z) als,t,u) =
Let f : R2 + R be defined by f(x,y) = |xy|e-(z?+y?). Evaluate SR2 f, if...
Let f : R2 + R be defined by f(x,y) = |xy|e-(z?+y?). Evaluate SR2 f, if it exists
what is the answer for number 4 1. Let r(t) = -i-e2t j + (t? +...
what is the answer for number
4
1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j +...
Whats the answer to number 1? 1. Let r(t) = -i-e2t j + (t? + 2t)k...
Whats the answer to number
1?
1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j + ick)...
2. Given R(x,y, z, w, k, t). There are two keys: (x,y) and z. Given the...
2. Given R(x,y, z, w, k, t). There are two keys: (x,y) and z. Given the following functional dependency: F = { {x,y} {z,w,k,t}, z {x,y,w,k,t }, yt}. Is R in 2nd normal form? Justify your answer. 3. Given R(x,y, z, w, k, t). There are two keys: (x,y) and z. Given the following functional dependency: F = { fd1:{x,y} {z,w,k,t}, fd2: z {x,y,w,k,t }, fd3:k x}. Is R in 3rd normal form? Justify your answer....
a - e (a) X + y +z = 11 X – Y – 2= -3...
a - e
(a) X + y +z = 11 X – Y – 2= -3 -2 + y - 2 = 5 (3x – y + 2z = 2 (b) x+y+z+t+p=17 X - Y - 2-t-p= -5 z +t+ p + y = 11 p - x - y = 1 -t + x = 10 (c) x +y + 2+t= -6 X - Y - 2 -t = 20 y - X=-39 2x + 3t + y -...
Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy +z-5, x = r + 2s,...
Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy +z-5, x = r + 2s, y = 2r - sec(s),z=s af Then is: ar a. r - sec(s) b. sec(s) c. r+s+sec(s) d. 4r + 4s - sec(s) a. b. d.
Consider F and C below. F(x, y, z) = yze?i + e'?j + xyek, C: r(t) - (t? + 1)i + (t? - 1)j + (t– 3t)k, Osts3 (a) pind a function f such that F – Vf. f(x, y, z) (b) Use part (a) to evaluate F. dr along the given curve C.
Let f(x,y,z) = xy + z-5,x=r +2s, y = 2r - sec(s), z = s Then I is: ar a. r - sec(s) b. sec(s) c. r+s+sec(s) d. 4r + 4s - sec(s) a. b. C. Given zº – xy + y2 + y2 = 2 and z is a differentiable function in x and y. Then at (1,1,1) is: дх a. 0 b. 1 c. d. e. None of the above o a. o b. ♡ C. o d.
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš sin () + yś sin () if xy + 0 242ADES if xy = 0 ii. Prove that every linear transformation T:R" - R" is continuous on R". iii. Let f:R" → R and a ER" Define Dis (a), the i-th partial derivative of f at a, 1 sisn. Determine whether the partial derivatives of f exist at (0,0) for the following function. In...
a(x,y,z) (1 point) Find the Jacobian. a(s,t,u) where x = 3t – 2s – 4u, y= -(2s + 4t+2u), z = 4t – 2s + 5u. 9 a(z,y,z) als,t,u) =
Let f : R2 + R be defined by f(x,y) = |xy|e-(z?+y?). Evaluate SR2 f, if it exists
what is the answer for number
4
1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j +...
Whats the answer to number
1?
1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j + ick)...
a - e
(a) X + y +z = 11 X – Y – 2= -3 -2 + y - 2 = 5 (3x – y + 2z = 2 (b) x+y+z+t+p=17 X - Y - 2-t-p= -5 z +t+ p + y = 11 p - x - y = 1 -t + x = 10 (c) x +y + 2+t= -6 X - Y - 2 -t = 20 y - X=-39 2x + 3t + y -...
Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy +z-5, x = r + 2s, y = 2r - sec(s),z=s af Then is: ar a. r - sec(s) b. sec(s) c. r+s+sec(s) d. 4r + 4s - sec(s) a. b. d.
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