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Consider F and C below. F(x, y, z) = (2xz + y²)i + 2xy j + (x² + 6z²)k C: x = t2, y = t + 1, z = - 3t 1, 0 ≤t≤ 1 (a) Find a function f such that F = Vf. (b) Use part (a) to evaluate fc Vf. dr along the given curve C.

Consider F and C below. F(x, y, z) = (2xz + y²)i + 2xy j + (x² + 6z²)k C: x = t2, y = t + 1, z = - 3t 1, 0 ≤t≤ 1 (a) Find a function f such that F = Vf. (b) Use part (a) to evaluate fc Vf. dr along the given curve C.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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Consider F and C below. F(x, y, z) = (2xz + y²)i + 2xy j + (x² + 6z²)k C: x = t2, y = t + 1, z = - 3t 1, 0 ≤t≤ 1 (a) Find a function f such that F = Vf. (b) Use part (a) to evaluate fc Vf. dr along the given curve C.
Transcribed Image Text:Consider F and C below. F(x, y, z) = (2xz + y²)i + 2xy j + (x² + 6z²)k C: x = t2, y = t + 1, z = - 3t 1, 0 ≤t≤ 1 (a) Find a function f such that F = Vf. (b) Use part (a) to evaluate fc Vf. dr along the given curve C.
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