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Math
Calculus
Calculus: Early Transcendentals
Chapter 14.1, Problem 67E
Chapter 14.1, Problem 67E
BUY
Calculus: Early Transcendentals
9th Edition
ISBN:
9780357598511
Author: James Stewart; Daniel K. Clegg; Saleem Watson
Publisher:
Cengage Learning US
expand_less
1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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14.1 Functions Of Several Variables
14.2 Limits And Continuity
14.3 Partial Derivatives
14.4 Tangent Planes And Linear Approximations
14.5 The Chain Rule
14.6 Directional Derivatives And The Gradient Vector
14.7 Maximum And Minimum Values
14.8 Lagrange Multipliers
Chapter Questions
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Problem 1E: If f(x,y)=x2y/2xy2 , find (a) f(1,3) (b) f(2,1) (c) f(x+h,y) (d) f(x,x)
Problem 2E: If g(x,y)=xsiny+ysinx , find (a) g(,0) (b) g(/2,/4) (c) g(0,y) (d) g(x,y+h)
Problem 3E
Problem 4E
Problem 5E: Let F(x,y,z)=yx2z . (a) Evaluate F(3,4,1) . (b) Find and describe the domain of F .
Problem 6E: Let f(x,y,z)=lnzx2+y2 . (a) Evaluate f(4,3,6) . (b) Find and describe the domain of f .
Problem 7E: Find and sketch the domain of the function. 7. f(x,y)=x2+y1
Problem 8E: Find and sketch the domain of the function. 8. f(x,y)=x3y4
Problem 9E: Find and sketch the domain of the function. 9. q(x,y)=x+44x2y2
Problem 10E: Find and sketch the domain of the function. 10. g(x,y)=lnx2+y29
Problem 11E: Find and sketch the domain of the function. 11. g(x,y)=xyx+y
Problem 12E: Find and sketch the domain of the function. 12. g(x,y)=ln(2x)1x2y2
Problem 13E: Find and sketch the domain of the function. 13. p(x,y)=xyx+1
Problem 14E: Find and sketch the domain of the function. 14. f(x,y)=sin1(x+y)
Problem 15E
Problem 16E: Find and sketch the domain of the function. 16. f(x,y,z)=ln164x24y2z2
Problem 17E: A model for the surface area of a human body is given by the function S = f(w, h) =...
Problem 18E
Problem 19E
Problem 20E: The temperature-humidity index I (or humidex, for short) is the perceived air temperature when the...
Problem 21E
Problem 22E: A company makes three sizes of cardboard boxes: small, medium, and large. It costs 2.50 to make a...
Problem 23E: Sketch the graph of the function. 23. f(x,y)=y
Problem 24E: Sketch the graph of the function. 24. f(x,y)=x2
Problem 25E: Sketch the graph of the function. 25. f(x,y)=104x5y
Problem 26E: Sketch the graph of the function. 26. f(x,y)=cosy
Problem 27E: Sketch the graph of the function. 27. f(x,y)=sinx
Problem 28E: Sketch the graph of the function. 28. f(x,y)=2x2y2
Problem 29E: Sketch the graph of the function. 29. f(x,y)=x2+4y2+1
Problem 30E: Sketch the graph of the function. 30. f(x,y)=4x2+y2
Problem 31E: Sketch the graph of the function. 31. f(x,y)=44x2y2
Problem 32E: Match the function with its graph (labeled IVI). Give reasons for your choices. (a)f(x,y)=11+x2+y2...
Problem 33E: A contour map for a function f is shown. Use it to estimate the values of f(3, 3) and f(3, 2). What...
Problem 34E
Problem 35E: Level curves (isothermals) are shown for the typical water temperature (in C) in Long Lake...
Problem 36E: Two contour maps are shown. One is for a function f whose graph is a cone. The other is for a...
Problem 37E: Locate the points A and B on the map of Lonesome Mountain (Figure 12). How would you describe the...
Problem 38E: Make a rough sketch of a contour map for the function whose graph is shown.
Problem 39E: The body mass index (BMI) of a person is defined by B(m,h)=mh2 where m is the persons mass (in...
Problem 40E: The body mass index is defined in Exercise 39. Draw the level curve of this function corresponding...
Problem 41E: A contour map of a function is shown. Use it to make a rough sketch of the graph of f. 41.
Problem 42E: A contour map of a function is shown. Use it to make a rough sketch of the graph of f. 42.
Problem 43E: A contour map of a function is shown. Use it to make a rough sketch of the graph of f. 43.
Problem 44E: A contour map of a function is shown. Use it to make a rough sketch of the graph of f. 44.
Problem 45E: Draw a contour map of the function showing several level curves. 45. f(x, y) = x2 y2
Problem 46E: Draw a contour map of the function showing several level curves. 46. f(x, y) = xy
Problem 47E: Draw a contour map of the function showing several level curves. 47. f(x,y)=x+y
Problem 48E: Draw a contour map of the function showing several level curves. 48. f(x, y) = ln(x2 + 4y2)
Problem 49E: Draw a contour map of the function showing several level curves. 49. f(x, y) = yex
Problem 50E: Draw a contour map of the function showing several level curves. 50. f(x, y) = y arctan x
Problem 51E: Draw a contour map of the function showing several level curves. 51. f(x,y)=x2+y23
Problem 52E: Draw a contour map of the function showing several level curves. 52. f(x, y) = y/(x2 + y2)
Problem 53E: Sketch both a contour map and a graph of the function and compare them. 53. f(x, y) = x2 + 9y2
Problem 54E: Sketch both a contour map and a graph of the function and compare them. 54. f(x,y)=369x24y2
Problem 55E: A thin metal plate, located in the xy-plane, has temperature T(x, y) at the point (x, y). Sketch...
Problem 56E: If V(x, y) is the electric potential at a point (x, y) in the xy-plane, then the level curves of V...
Problem 57E
Problem 58E
Problem 59E
Problem 60E: Graph the function using various domains and viewpoints. If your software also produces level...
Problem 61E: Match the function (a) with its graph (labeled AF below) and (b) with its contour map (labeled IVI)....
Problem 62E: Match the function (a) with its graph (labeled AF below) and (b) with its contour map (labeled IVI)....
Problem 63E: Match the function (a) with its graph (labeled AF below) and (b) with its contour map (labeled IVI)....
Problem 64E: Match the function (a) with its graph (labeled AF below) and (b) with its contour map (labeled IVI)....
Problem 65E: Match the function (a) with its graph (labeled AF below) and (b) with its contour map (labeled IVI)....
Problem 66E: Match the function (a) with its graph (labeled AF below) and (b) with its contour map (labeled IVI)....
Problem 67E
Problem 68E: Describe the level surfaces of the function. 68. g(x,y,z)=x+y2z2
Problem 69E
Problem 70E
Problem 71E: Describe how the graph of g is obtained from the graph of f. 71. (a) g(x, y) = f(x, y) + 2 (b) g(x,...
Problem 72E: Describe how the graph of g is obtained from the graph of f. 72. (a) g(x, y) = f(x 2, y) (b) g(x,...
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E: Investigate the family of functions f(x,y)=ecx2+y2. How does the shape of the graph depend on c?
Problem 78E
Problem 79E
Problem 80E: Graph the functions f(x,y)=x2+y2 f(x,y)=ex2+y2 f(x,y)=lnx2+y2 f(x,y)=sin(x2+y2) and f(x,y)=1x2+y2 In...
Problem 81E
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