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Math
Calculus
Calculus, Early Transcendentals
Chapter 14.3, Problem 3E
Chapter 14.3, Problem 3E
BUY
Calculus, Early Transcendentals
9th Edition
ISBN:
9781337613927
Author: Stewart
Publisher:
CENGAGE L
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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: At the beginning of this section we discussed the function I = f(T, H), where I is the heat index, T...
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E: A contour map is given for a function f. Use it to estimate fx(2, 1) and fy(2, 1).
Problem 7E: If f(x, y) = 16 4x2 y2, find fx(1, 2) and fy(1, 2) and interpret these numbers as slopes....
Problem 8E: If f(x,y)=4x24y2, find fx(1,0) and fy(1, 0) and interpret these numbers as slopes. Illustrate with...
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E: Find the indicated partial derivative. 42. f(x,y)=ysin1(x,y);fy(1,12)
Problem 39E: Find the indicated partial derivative. 43. f(x,y,z)=ln1x2+y2+z21+x2+y2+z2;fy(1,2,2)
Problem 40E: Find the indicated partial derivative. 44. f(x, y, z) = xyz; fz(e, 1, 0)
Problem 41E: Use implicit differentiation to find z/x and z/y . 41. x2+2y2+3z2=1
Problem 42E: Use implicit differentiation to find z/x and z/y . 42. x2y2+z22z=4
Problem 43E: Use implicit differentiation to find z/x and z/y . 43. ez=xyz
Problem 44E: Use implicit differentiation to find z/x and z/y . 44. yz+xlny=z2
Problem 45E: Find z/x and z/y. 51. (a) z = f(x) + g(y) (b) z = f(x + y)
Problem 46E: Find z/x and z/y. 52. (a) z = f(x)g(y) (b) z = f(xy) (c) z = f(x/y)
Problem 47E
Problem 48E: Find all the second partial derivatives. 54. f(x, y) = ln(ax + by)
Problem 49E: Find all the second partial derivatives. 55. z=y2z+3y
Problem 50E
Problem 51E
Problem 52E
Problem 53E: Verify that the conclusion of Clairauts Theorem holds, that is, uxy = uyx. 59. u = x4y3 y4
Problem 54E: Verify that the conclusion of Clairauts Theorem holds, that is, uxy = uyx. 60. u = exy sin y
Problem 55E: Verify that the conclusion of Clairauts Theorem holds, that is, uxy = uyx. 61. u = cos(x2y)
Problem 56E: Verify that the conclusion of Clairauts Theorem holds, that is, uxy = uyx. 62. u = ln(x + 2y)
Problem 57E: Find the indicated partial derivative(s). 63. f(x, y) = x4y2 x3y; fxxx, fxyx
Problem 58E: Find the indicated partial derivative(s). 64. f(x, y) = sin(2x + 5y); fyxy
Problem 59E: Find the indicated partial derivative(s). 65. f(x,y,z)=exyz2;fxyz
Problem 60E
Problem 61E: Find the indicated partial derivative(s). 67. w=u+v2;3Wu2v
Problem 62E
Problem 63E: Find the indicated partial derivative(s). 69. w=xy+2z;3wzyx,3wx2y
Problem 64E: Find the indicated partial derivative(s). 70. u = xaybzc; 6uxy2z3
Problem 65E: Use Definition 4 to find fx(x,y) and fy(x,y) . 65. f(x,y)=xy2x3y
Problem 66E: Use Definition 4 to find fx(x,y) and fy(x,y) . 66. f(x,y)=xx+y2
Problem 67E: If f(x,y,z)=xy2z3+arcsin(xz), find fxzy. [Hint: Which order of differentiation is easiest?]
Problem 68E: If g(x,y,z)=1+xz+1xy, find gxyz. [Hint: Which order of differentiation is easiest?]
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E: Use the table of values of f(x, y) to estimate the values of fx(3, 2), fx(3, 2.2),and fxy(3, 2).
Problem 74E
Problem 75E
Problem 76E: If u=ea1x1+a2x2++anxn, where a12+a22++an2=1, show that 2ux12+2ux22++2uxn2=u
Problem 77E: Show that the function u=u(x,t) is a solution of the wave equation utt=a2uxx . (a) u=sin(kx)sin(akt)...
Problem 78E
Problem 79E: Verify that the function u=1/x2+y2+z2 is a solution of the three-dimensional Laplace equation uxx +...
Problem 80E
Problem 81E: The Diffusion Equation The diffusion equation ct=D2cx2 where D is a positive constant, describes the...
Problem 82E
Problem 83E
Problem 84E
Problem 85E: Show that the Cobb-Douglas production function satisfies P(L, K0) = C1(K0)L by solving the...
Problem 86E
Problem 87E
Problem 88E
Problem 89E: In the project following Section 4.7 we expressed the power needed by a bird during its flapping...
Problem 90E
Problem 91E
Problem 92E
Problem 93E: The ellipsoid 4x2+2y2+z2=16 intersects the plane y=2 in an ellipse. Find parametric equations for...
Problem 94E
Problem 95E
Problem 96E: If a, b, c are the sides of a triangle and A, B, C are the opposite angles, find A/a, A/b, A /c by...
Problem 97E
Problem 98E
Problem 99E: If f(x,y)=x(x2+y2)3/2esin(x2y) find fx(1,0). [Hint: Instead of finding fx(x, y) first, note that...
Problem 100E: If f(x,y)=x3+y33 find fx(0, 0).
Problem 101E
Problem 1DP
Problem 2DP
Problem 3DP
Problem 4DP
Problem 5DP
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