y2 %3D 1. 60. x²y dx dy dz, T: Region bounded by 4

Calculus: Early Transcendentals
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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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I want solution of Question no 60.
Functions of Several Real Variables 2.
57.
xy z dx dy dz, T: Region bounded by x + y + z = 1 and the coordinate planes.
58.
xyz dx dy dz, T: Region bounded by x +y +
= 8 and the coordinate planes.
59.
xy2z dx dy dz, T: Region bounded by x + y + z* = 1.
60.
x'y dx dy dz, T: Region bounded by * ++
2.7
Answers and Hints
Exercise 2.1
1. I f (x, y) - 11 = 1 (x- 1) +(y- 1) + 2(x – 1) + 2(y - 1)I
<lx-1P+ly-1P+21x-11+ 2 l y – 1|< ɛ
(i) if Ix-11<8, 1 y-11< 8 is used, we get 282+ 48< e or 8< [/(E+ 2)/2 – 1]
(ii) if 82 < 8 is used, we get &< e/6
(iii) if (x - 1)2 + (y- 1) < 8² and lx-11< 6, l y-11< 8 is used, we get 8< VE+4-2.
2. If (x, y) - 71 =1 (x- 2) - (y- 1) + 6(x- 2)- 2(y- 1)I
<lx- 2 P+ly-If+61x-21+21ly-11<e.
(i) if Ix- 21< 8, 1 y- 11< 8 is used, we get 282 + 88 < ɛ, or 8< JCe+8)/2 – 2.n
Transcribed Image Text:Functions of Several Real Variables 2. 57. xy z dx dy dz, T: Region bounded by x + y + z = 1 and the coordinate planes. 58. xyz dx dy dz, T: Region bounded by x +y + = 8 and the coordinate planes. 59. xy2z dx dy dz, T: Region bounded by x + y + z* = 1. 60. x'y dx dy dz, T: Region bounded by * ++ 2.7 Answers and Hints Exercise 2.1 1. I f (x, y) - 11 = 1 (x- 1) +(y- 1) + 2(x – 1) + 2(y - 1)I <lx-1P+ly-1P+21x-11+ 2 l y – 1|< ɛ (i) if Ix-11<8, 1 y-11< 8 is used, we get 282+ 48< e or 8< [/(E+ 2)/2 – 1] (ii) if 82 < 8 is used, we get &< e/6 (iii) if (x - 1)2 + (y- 1) < 8² and lx-11< 6, l y-11< 8 is used, we get 8< VE+4-2. 2. If (x, y) - 71 =1 (x- 2) - (y- 1) + 6(x- 2)- 2(y- 1)I <lx- 2 P+ly-If+61x-21+21ly-11<e. (i) if Ix- 21< 8, 1 y- 11< 8 is used, we get 282 + 88 < ɛ, or 8< JCe+8)/2 – 2.n
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