Consider F and C below.
F(x, y, z) =

2xz + y2

i + 2xy j +

x2 + 15z2

k

C: x = t2, y = t + 1, z = 3t − 1, 0 ≤ t ≤ 1
(a) Find a function f such that F = ∇f.
f(x, y, z) =

Correct: Your answer is correct.

(b) Use part (a) to evaluate

C
∇f · dr
along the given curve C.

Question

13-07-2024
Mathematics

Answered

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Consider F and C below.
F(x, y, z) =

2xz + y2

i + 2xy j +

x2 + 15z2

k

C: x = t2, y = t + 1, z = 3t − 1, 0 ≤ t ≤ 1
(a) Find a function f such that F = ∇f.
f(x, y, z) =

Correct: Your answer is correct.

(b) Use part (a) to evaluate

C
∇f · dr
along the given curve C.

Sagot :

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Consider F and C below. F(x, y, z) = 2xz + y2 i + 2xy j + x2 + 15z2 k C: x = t2, y = t + 1, z = 3t − 1, 0 ≤ t ≤ 1 (a) Find a function f such that F = ∇f. f(x, y, z) = Correct: Your answer is correct. (b) Use part (a) to evaluate C ∇f · dr along the given curve C.

Sagot :

Other Questions

Consider F and C below.
F(x, y, z) =

2xz + y2

i + 2xy j +

x2 + 15z2

k

C: x = t2, y = t + 1, z = 3t − 1, 0 ≤ t ≤ 1
(a) Find a function f such that F = ∇f.
f(x, y, z) =

Correct: Your answer is correct.

(b) Use part (a) to evaluate

C
∇f · dr
along the given curve C.