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)? the same length as (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 7f.dr = (d) If C is any piecewise-smooth path from S to P, then Vf-dr (e) If C is any piecewise-smooth closed path from P to Q to T to S to P, then Vf.dr = 3 y 2 3 (Click on graph to enlarge) 41 35 29

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
Question
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)?
the same length as
(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
7f.dr =
(d) If C is any piecewise-smooth path from S to P, then
Vf-dr
(e) If C is any piecewise-smooth closed path from P to Q to T to S to P, then
Vf.dr =
3
y
2
3
(Click on graph to enlarge)
41
35
29
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)? the same length as (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 7f.dr = (d) If C is any piecewise-smooth path from S to P, then Vf-dr (e) If C is any piecewise-smooth closed path from P to Q to T to S to P, then Vf.dr = 3 y 2 3 (Click on graph to enlarge) 41 35 29
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