Suppose that w = f(x, y, z), x = e"s, y = s², and z = r cos(rs). (a) Use the Chain Rule to write down formulas for and dr ds (b) Given that wr(1,4,0) = 3, w,(1,4,0) = 2, and wz(1,4, 0) = -3, find the value of and when dr ds r = 0 and s = 2.

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
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Chapter6: Topics In Analytic Geometry
Section6.4: Hyperbolas
Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
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Suppose that w =
f (x, y, z), x = e"s, y= s², and z = r cos(rs).
dw
dw
and
dr
(a) Use the Chain Rule to write down formulas for
ds
(b) Given that w4(1,4,0) = 3, w,(1,4,0) = 2, and wz(1,4, 0) = –3, find the value of
dr
dw
when
ds
and
r = 0 and s = 2.
Transcribed Image Text:Suppose that w = f (x, y, z), x = e"s, y= s², and z = r cos(rs). dw dw and dr (a) Use the Chain Rule to write down formulas for ds (b) Given that w4(1,4,0) = 3, w,(1,4,0) = 2, and wz(1,4, 0) = –3, find the value of dr dw when ds and r = 0 and s = 2.
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