 12.1: Each edge of a cubical box has length 1 m. The box contains nine sp...
 12.2: Let B be a solid box with length L, width W, and height H. Let S be...
 12.3: Let L be the line of intersection of the planes cx 1 y 1 z c and x ...
 12.4: A plane is capable of flying at a speed of 180 kmyh in still air. T...
 12.5: Suppose v1 and v2 are vectors with  v1  2,  v2  3, and v1 ? v2 ...
 12.6: Find an equation of the largest sphere that passes through the poin...
 12.7: Suppose a block of mass m is placed on an inclined plane, as shown ...
 12.8: A solid has the following properties. When illuminated by rays para...
Solutions for Chapter 12: Calculus 8th Edition
Full solutions for Calculus  8th Edition
ISBN: 9781285740621
Solutions for Chapter 12
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Calculus was written by and is associated to the ISBN: 9781285740621. Chapter 12 includes 8 full stepbystep solutions. Since 8 problems in chapter 12 have been answered, more than 9525 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus, edition: 8.

Bar chart
A rectangular graphical display of categorical data.

Complex number
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)

Definite integral
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

Divisor of a polynomial
See Division algorithm for polynomials.

Even function
A function whose graph is symmetric about the yaxis for all x in the domain of ƒ.

First quartile
See Quartile.

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Graph of parametric equations
The set of all points in the coordinate plane corresponding to the ordered pairs determined by the parametric equations.

kth term of a sequence
The kth expression in the sequence

Magnitude of a vector
The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2

Parameter interval
See Parametric equations.

Permutation
An arrangement of elements of a set, in which order is important.

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Radian measure
The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

Random variable
A function that assigns realnumber values to the outcomes in a sample space.

Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.

Summation notation
The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series

Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.

Zero matrix
A matrix consisting entirely of zeros.