Consider F and C below. F(x, y, z) = (2xz + y²)i + 2xyj + (x² + 12z²) k C: x = t², y = t + 3, z = 2t – 1, 0≤t≤1 (a) Find a function f such that F = Vf. f(x, y, z): = =[" C (b) Use part (a) to evaluate Vf. dr along the given curve C.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 14BEXP
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Consider F and C below.
F(x, y, z) = (2xz + y²)i + 2xyj + (x² + 12z²) k
C: x = t², y = t + 3, z = 2t − 1, 0 ≤ t ≤ 1
(a) Find a function of such that F
f(x, y, z)
=
(b) Use part (a) to evaluate
So
= Vf.
Vf. dr along the given curve C.
Transcribed Image Text:Consider F and C below. F(x, y, z) = (2xz + y²)i + 2xyj + (x² + 12z²) k C: x = t², y = t + 3, z = 2t − 1, 0 ≤ t ≤ 1 (a) Find a function of such that F f(x, y, z) = (b) Use part (a) to evaluate So = Vf. Vf. dr along the given curve C.
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