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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Question
How do you solve 5? Show steps
Transcribed Image Text:CHAPTER SUMMA
utility (sa
x DVDS and y video games
U(x, y) = In (x²Vy)
If each DVD costs $20 and each video game costs
$50, how many DVDS and video games should he
purchase to maximize utility?
portion of
0 < y < 1.
What of A B will the
10. LEAST-SQUARES
PROFIT DATA A
millions of dollars)
8. MEDICINE A certain disease can be treated by
administering at least 70 units of drug C, but that
level of medication sometimes results in serious
side effects. Looking for a safer approach, a
physician decides instead to use drugs A and B,
which result in no side effects as long as their
combined dosage is less than 60 units. Moreover,
she determines that when x units of drug A and
units of drug B are administered to a patient, the
effect is equivalent to administering E units of
drug C, where
operation is shown
Year
1.
Profit (millions
of dollars)
1.03
a. Plot these dat:
b. Find the equa
E = 0.05(xy – 2x2 – y² + 95x + 20y)
through the d
%3D
-
c.
Use the least
equivalent level E of drug C? If the physician
administers the optimum dosages of drugs A and B,
company's 6
Review Exercises
DECA
In Exercises 1 through 10, find the partial derivatives fx
and fy.
For each of the fu
compute the second
and fyx
1. f(x, y) = 2r°y + 3xy? + 2
%3D
11. f(x, y) =
2. f(x, y) = (xy² + 1)
3. f(x, y) = Vx(x – y³)
4. f(x, y) = xe + ye¯*
%3D
12. f(x, y) = x² -
13. f(x, y) = x In
%3D
%3D
%3D
14. = (5x
f(x, y)
%3D
5. f(x, y) =
15. For each of
-
6. f(x, y) = x In(x² – y) + y ln(y - 2r)
level curves
X 3=
a. f(x, y)
.3
7. f(x, y)
%3D
b. ƒ(x, y)
8. f(x, y) = xye"
16. For each c
%3D
indicated
= (K °x)f °6
2x + y
%3D
= (K *x)f °0[
x + 3y
b. f(x, y
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