- 13.1: A particle P moves with constant angular speed around a circle whos...
- 13.2: A circular curve of radius R on a highway is banked at an angle so ...
- 13.3: A projectile is fired from the origin with angle of elevation and i...
- 13.4: (a) A projectile is fired from the origin down an inclined plane th...
- 13.5: A ball rolls off a table with a speed of 2 ftys. The table is 3.5 f...
- 13.6: Find the curvature of the curve with parametric equations x y t 0 s...
- 13.7: If a projectile is fired with angle of elevation and initial speed ...
- 13.8: A cable has radius r and length L and is wound around a spool with ...
- 13.9: Show that the curve with vector equation rstd ka1t 2 1 b1t 1 c1, a2...
Solutions for Chapter 13: Calculus 8th Edition
Full solutions for Calculus | 8th Edition
Composition of functions
(f ? g) (x) = f (g(x))
A measure of the strength of the linear relationship between two variables, pp. 146, 162.
The function y = csc x
Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x) - ƒ(a) x - a provided the limit exists
Directed line segment
A statement of equality between two expressions.
Graph of an equation in x and y
The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.
Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.
Index of summation
See Summation notation.
Law of cosines
a2 = b2 + c2 - 2bc cos A, b2 = a2 + c2 - 2ac cos B, c2 = a2 + b2 - 2ab cos C
One-to-one rule of logarithms
x = y if and only if logb x = logb y.
See Parametric equations.
Right circular cone
The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.
Second-degree equation in two variables
Ax 2 + Bxy + Cy2 + Dx + Ey + F = 0, where A, B, and C are not all zero.
A visualization of the Multiplication Principle of Probability.
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.
A vector that specifies the motion of an object in terms of its speed and direction.
Vertical stretch or shrink
See Stretch, Shrink.
A point that lies on both the graph and the y-axis.