- PS.1: Find the volume of the solid of intersection of the three cylinders...
- PS.2: Let and be positive real numbers. The first octant of theplane is s...
- PS.3: Derive Eulers famous result that was mentioned in Section 9.3,by co...
- PS.4: Consider a circular lawn with a radius of 10 feet, as shown inthe f...
- PS.5: The figure shows the region bounded by the curvesand Use the change...
- PS.6: The figure shows a solid bounded below by the plane andabove by the...
- PS.7: Sketch the solid whose volume is given by the sum of theiterated in...
- PS.8: Prove that limn 10 10xn yn dx dy 0.
- PS.9: In Exercises 9 and 10, evaluate the integral. (Hint: See Exercise69...
- PS.10: In Exercises 9 and 10, evaluate the integral. (Hint: See Exercise69...
- PS.11: Consider the functionFind the relationship between the positive con...
- PS.12: Find the volume of the solid generated by revolving the regionin th...
- PS.13: From 1963 to 1986, the volume of the Great Salt Lake approximatelyt...
- PS.14: The angle between a plane and the plane is whereThe projection of a...
- PS.15: Use the result of Exercise 14 to order the planes in ascendingorder...
- PS.16: Evaluate the integral 0 011 x2 y22 dx dy.
- PS.17: Evaluate the integrals
- PS.18: Show that the volume of a spherical block can be approximatedbyV 2 sin
Solutions for Chapter PS: Multiple Integration
Full solutions for Calculus | 9th Edition
Absolute value of a vector
See Magnitude of a vector.
Addition property of inequality
If u < v , then u + w < v + w
Additive identity for the complex numbers
0 + 0i is the complex number zero
Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.
A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined
A logarithm with base 10.
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists
Directed line segment
A function whose domain is the first n positive integers for some fixed integer n.
Inverse reflection principle
If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.
Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.
Multiplication principle of counting
A principle used to find the number of ways an event can occur.
The numbers 1, 2, 3, . . . ,.
A square matrix with nonzero determinant
Projection of u onto v
The vector projv u = au # vƒvƒb2v
tan ?= sin ?cos ?and cot ?= cos ? sin ?
Standard form of a complex number
a + bi, where a and b are real numbers
Stemplot (or stem-and-leaf plot)
An arrangement of a numerical data set into a specific tabular format.
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.
The points (0, y, z) in Cartesian space.