In Exercises 7- 12, functions z = f(x, y), x = g(t) and y = h(t) are given. dz (a) Use the Multivariable Chain Rule to compute dz at the indicated t-value. dt (b) Evaluate 7. z 3x+4y, x=t, y = 2t; t= 1 8. =x-y. y =t-1; x=t, t=1

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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In Exercises 7- 12, functions z =
f(x, y), x = g(t) and
এ(0) nd
y=h(t) are given.
dz
(a) Use the Multivariable Chain Rule to compute
dz
at the indicated t-value.
dt
(b) Evaluate
7. z 3x+4y,
y= 2t;
t=1
8.? =x -y,
y =r-1;
x=t,
t=1
9. z Sx + 2y, x= 2 cost+1, y sin t- 3; t=/4
10. Z=
x= Cos t,
y = sin t;
t==/2
y+1"
11. z=x + 2y,
x= sin t,
y= 3 sin t
t=T/4
12. z = çosx sin y.
y= 2 t /2;
t= 3
Transcribed Image Text:Problems In Exercises 7- 12, functions z = f(x, y), x = g(t) and এ(0) nd y=h(t) are given. dz (a) Use the Multivariable Chain Rule to compute dz at the indicated t-value. dt (b) Evaluate 7. z 3x+4y, y= 2t; t=1 8.? =x -y, y =r-1; x=t, t=1 9. z Sx + 2y, x= 2 cost+1, y sin t- 3; t=/4 10. Z= x= Cos t, y = sin t; t==/2 y+1" 11. z=x + 2y, x= sin t, y= 3 sin t t=T/4 12. z = çosx sin y. y= 2 t /2; t= 3
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