The figure shows level curves of a function f(x, y). (a) Draw gradient vectors at P and Q. Is Vf(P) longer than, shorter than, or the same length as Vf(Q)? ? (b) If C is the line segment from P to Q, then S Vf.dr = (c) If C is any piecewise-smooth path from P to T to Q, then for Vf.dr = (d) If C is any piecewise-smooth path from S to P, then Jo Vf.dr = (e) If C is any piecewise-smooth closed path from P to Q to T to S to P, then √vf.dr = 0 y (Click on granh t 17 14 11 X

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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The figure shows level curves of a function f(x, y).
(a) Draw gradient vectors at P and Q. Is Vf(P) longer than, shorter than, or the same length as Vf(Q)?
?
(b) If C is the line segment from P to Q, then
√
Vf.dr =
(c) If C is any piecewise-smooth path from P to T to Q, then
for Vf.dr =
(d) If C is any piecewise-smooth path from S to P, then
Jo Vf-dr
(e) If C is any piecewise-smooth closed path from P to Q to T to S to P, then
[vƒ•dř=0
y
(Click on granh t
17
14
X
Transcribed Image Text:The figure shows level curves of a function f(x, y). (a) Draw gradient vectors at P and Q. Is Vf(P) longer than, shorter than, or the same length as Vf(Q)? ? (b) If C is the line segment from P to Q, then √ Vf.dr = (c) If C is any piecewise-smooth path from P to T to Q, then for Vf.dr = (d) If C is any piecewise-smooth path from S to P, then Jo Vf-dr (e) If C is any piecewise-smooth closed path from P to Q to T to S to P, then [vƒ•dř=0 y (Click on granh t 17 14 X
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