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Math
Calculus
University Calculus: Early Transcendentals (4th Edition)
Chapter 13.1, Problem 80E
Chapter 13.1, Problem 80E
BUY
University Calculus: Early Transcendentals (4th Edition)
4th Edition
ISBN:
9780134995540
Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.
Publisher:
PEARSON
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1 Functions
2 Limits And Continuity
3 Derivatives
4 Application Of Derivatives
5 Integrals
6 Applications Of Definite Integrals
7 Integrals And Trascendental Functions
8 Techniques Of Integration
9 Infinite Sequences And Series
10 Parametric Equations And Polar Coordinates
11 Vectors And The Geometry Of Space
12 Vector-valued Functions And Motion In Space
13 Partial Derivatives
14 Multiple Integrals
15 Integrals And Vector Fields
16 First-order Differential Equations
17 Second-order Differential Equations
A.1 Real Numbers And The Real Line
A.2 Mathematical Induction
A.3 Lines And Circles
A.4 Conic Sections
A.5 Proofs Of Limit Theorems
A.6 Commonly Occurring Limits
A.7 Theory Of The Real Numbers
A.8 Complex Numbers
A.9 The Distributive Law For Vector Cross Products
A.10 The Mixed Derivative Theorem And The Increment Theorem
B.1 Relative Rates Of Growth
B.2 Probability
B.3 Conics In Polar Coordinates
B.4 Taylor's Formula For Two Variables
B.5 Partial Derivatives With Constrained Variables
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13.1 Functions Of Several Variables
13.2 Limits And Continuity In Higher Dimensions
13.3 Partial Derivatives
13.4 The Chain Rule
13.5 Directional Derivatives And Gradient Vectors
13.6 Tangent Planes And Differentials
13.7 Extreme Values And Saddle Points
13.8 Lagrange Multipliers
Chapter Questions
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Problem 1E: In Exercises 1–4, find the specific function values. 1. f(x, y) = x2 + xy3 f(0, 0) f(−1, 1) f(2,...
Problem 2E: In Exercises 1–4, find the specific function values. 2. f(x, y) = sin (xy)
Problem 3E: In Exercises 1–4, find the specific function values. 3. f(3, −1, 2) f(2, 2, 100)
Problem 4E: In Exercises 1–4, find the specific function values. 4. f(0, 0, 0) f(2, −3, 6) f(−1, 2, 3)
Problem 5E: In Exercises 5–12, find and sketch the domain for each function. 5.
Problem 6E: In Exercises 5–12, find and sketch the domain for each function. 6. f(x, y) = ln(x2 + y2 − 4)
Problem 7E: In Exercises 512, find and sketch the domain for each function. 7. f(x,y)=(x1)(y+2)(yx)(yx3)
Problem 8E
Problem 9E: In Exercises 5–12, find and sketch the domain for each function. 9. f(x, y) = cos−1 (y − x2)
Problem 10E
Problem 11E: In Exercises 512, find and sketch the domain for each function. 11. f(x,y)=(x24)(y29)
Problem 12E
Problem 13E: In Exercises 1316, find and sketch the level curves f(x, y) = c on the same set of coordinate axes...
Problem 14E: In Exercises 13–16, find and sketch the level curves f(x, y) = c on the same set of coordinate axes...
Problem 15E: In Exercises 13–16, find and sketch the level curves f(x, y) = c on the same set of coordinate axes...
Problem 16E
Problem 17E: In Exercises 17-30, (a) find the function’s domain, (b) find the function’s range, (c) describe the...
Problem 18E: In Exercises 17-30, (a) find the function’s domain, (b) find the function’s range, (c) describe the...
Problem 19E: In Exercises 17-30, (a) find the function’s domain, (b) find the function’s range, (c) describe the...
Problem 20E: In Exercises 17-30, (a) find the function’s domain, (b) find the function’s range, (c) describe the...
Problem 21E: In Exercises 17-30, (a) find the function’s domain, (b) find the function’s range, (c) describe the...
Problem 22E: In Exercises 17-30, (a) find the function’s domain, (b) find the function’s range, (c) describe the...
Problem 23E: In Exercises 17-30, (a) find the function’s domain, (b) find the function’s range, (c) describe the...
Problem 24E: In Exercises 17-30, (a) find the function’s domain, (b) find the function’s range, (c) describe the...
Problem 25E: In Exercises 17-30, (a) find the function’s domain, (b) find the function’s range, (c) describe the...
Problem 26E: In Exercises 17-30, (a) find the function’s domain, (b) find the function’s range, (c) describe the...
Problem 27E: In Exercises 17-30, (a) find the function’s domain, (b) find the function’s range, (c) describe the...
Problem 28E
Problem 29E
Problem 30E
Problem 31E: Exercises 31–36 show level curves for six functions. The graphs of these functions are given on the...
Problem 32E: Exercises 31–36 show level curves for six functions. The graphs of these functions are given on the...
Problem 33E: Exercises 31–36 show level curves for six functions. The graphs of these functions are given on the...
Problem 34E: Exercises 31–36 show level curves for six functions. The graphs of these functions are given on the...
Problem 35E: Exercises 31–36 show level curves for six functions. The graphs of these functions are given on the...
Problem 36E: Exercises 31–36 show level curves for six functions. The graphs of these functions are given on the...
Problem 37E: Display the values of the functions in Exercises 37–48 in two ways: (a) by sketching the surface z =...
Problem 38E: Display the values of the functions in Exercises 37–48 in two ways: (a) by sketching the surface z =...
Problem 39E: Display the values of the functions in Exercises 37–48 in two ways: (a) by sketching the surface z =...
Problem 40E: Display the values of the functions in Exercises 37–48 in two ways: (a) by sketching the surface z =...
Problem 41E
Problem 42E
Problem 43E: Display the values of the functions in Exercises 37–48 in two ways: (a) by sketching the surface z =...
Problem 44E
Problem 45E: Display the values of the functions in Exercises 37–48 in two ways: (a) by sketching the surface z =...
Problem 46E
Problem 47E: Display the values of the functions in Exercises 37–48 in two ways: (a) by sketching the surface z =...
Problem 48E
Problem 49E: In Exercises 49–52, find an equation for, and sketch the graph of, the level curve of the function...
Problem 50E: In Exercises 49–52, find an equation for, and sketch the graph of, the level curve of the function...
Problem 51E: In Exercises 49–52, find an equation for, and sketch the graph of, the level curve of the function...
Problem 52E: In Exercises 49–52, find an equation for, and sketch the graph of, the level curve of the function...
Problem 53E: In Exercises 53–60, sketch a typical level surface for the function. 53. f(x, y, z) = x2 + y2 + z2
Problem 54E
Problem 55E: In Exercises 53–60, sketch a typical level surface for the function. 55.
Problem 56E
Problem 57E
Problem 58E
Problem 59E: In Exercises 53–60, sketch a typical level surface for the function. 59.
Problem 60E: In Exercises 53–60, sketch a typical level surface for the function. 60.
Problem 61E: In Exercises 61–64, find an equation for the level surface of the function through the given...
Problem 62E: In Exercises 61–64, find an equation for the level surface of the function through the given...
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
Problem 80E
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