- 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
A rectangular graphical display of categorical data.
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)
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.
A function whose graph is symmetric about the y-axis for all x in the domain of ƒ.
First-degree 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
See Parametric equations.
An arrangement of elements of a set, in which order is important.
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
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.
A function that assigns real-number values to the outcomes in a sample space.
Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.
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.
A matrix consisting entirely of zeros.