28. Suppose you follow the spiral path C: x = cos t, y= sin t, and z= t, for t20, through the domain of the function xyz w = f(x,y,z) = 2 +1 Complete parts (a) and (b) below. First, find some intermediate derivatives. dw dx (Type an expression using x, y, and z as the variables.) dx %3D dt (Type an expression using t as the variable.) dw %3D ду (Type an expression using x, y, and z as the variables.)
28. Suppose you follow the spiral path C: x = cos t, y= sin t, and z= t, for t20, through the domain of the function xyz w = f(x,y,z) = 2 +1 Complete parts (a) and (b) below. First, find some intermediate derivatives. dw dx (Type an expression using x, y, and z as the variables.) dx %3D dt (Type an expression using t as the variable.) dw %3D ду (Type an expression using x, y, and z as the variables.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![28. Suppose you follow the spiral path C: x = cos t, y = sin t, and z=t, for t20, through the domain of the function
xyz
w = f(x,y,z) =
z +1
Complete parts (a) and (b) below.
First, find some intermediate derivatives.
dw
dx
(Type an expression using x, y, and z as the variables.)
dx
dt
(Type an expression using t as the variable.)
dw
dy
(Type an expression using x, y, and z as the variables.)
dy
dt
(Type an expression using t as the variable.)
dw
%3D
dz
(Type an expression using x, y, and z as the variables.)
dz
dt
(Type an expression using t as the variable.)
(a) Find w'(t) along C.
dw
%3D
(Type an expression using t as the variable.)
(b) Estimate the point (x,y,z) on C at which w has its maximum value.
(x,y,z) =
(Type integers or decimals rounded to the nearest thousandth as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c6e41b2-48f8-48f8-9e99-525c35ddf3fa%2Fe10d889b-a6c6-4de0-afa9-e54b9465b02d%2Fe7qrynm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:28. Suppose you follow the spiral path C: x = cos t, y = sin t, and z=t, for t20, through the domain of the function
xyz
w = f(x,y,z) =
z +1
Complete parts (a) and (b) below.
First, find some intermediate derivatives.
dw
dx
(Type an expression using x, y, and z as the variables.)
dx
dt
(Type an expression using t as the variable.)
dw
dy
(Type an expression using x, y, and z as the variables.)
dy
dt
(Type an expression using t as the variable.)
dw
%3D
dz
(Type an expression using x, y, and z as the variables.)
dz
dt
(Type an expression using t as the variable.)
(a) Find w'(t) along C.
dw
%3D
(Type an expression using t as the variable.)
(b) Estimate the point (x,y,z) on C at which w has its maximum value.
(x,y,z) =
(Type integers or decimals rounded to the nearest thousandth as needed.)
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