- 12.R.1E: State the rules for differentiating and integrating vector function...
- 12.R.2E: How do you define and calculate the velocity, speed, direction of m...
- 12.R.3E: What is special about the derivatives of vector functions of consta...
- 12.R.4E: What are the vector and parametric equations for ideal projectile m...
- 12.R.5E: How do you define and calculate the length of a segment of a smooth...
- 12.R.6E: How do you measure distance along a smooth curve in space from a pr...
- 12.R.7E: What is a differentiable curve’s unit tangent vector? Give an example.
- 12.R.8E: Define curvature, circle of curvature (osculating circle), center o...
- 12.R.9E: What is a plane curve’s principal normal vector? When is it defined...
- 12.R.10E: How do you define N and for curves in space? How are these quantiti...
- 12.R.11E: What is a curve’s binormal vector? Give an example. How is this vec...
- 12.R.12E: What formulas are available for writing a moving body’s acceleratio...
- 12.R.13E: State Kepler’s laws.
Solutions for Chapter 12.R: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals | 2nd Edition
artesian coordinate system
An association between the points in a plane and ordered pairs of real numbers; or an association between the points in three-dimensional space and ordered triples of real numbers
Decreasing on an interval
A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)
Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)
A number that is associated with a square matrix
a b = aa 1 b b, b Z 0
See Equilibrium point.
A function of the form ƒ(x) = a ? bx,where ?0, b > 0 b ?1
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).
Horizontal Line Test
A test for determining whether the inverse of a relation is a function.
The numbers . . ., -3, -2, -1, 0,1,2,...2
Multiplication principle of counting
A principle used to find the number of ways an event can occur.
Real numbers shown to the left of the origin on a number line.
Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,
Two points that are symmetric with respect to a lineor a point.
Set of all possible outcomes of an experiment.
Standard form of a polynomial function
ƒ(x) = an x n + an-1x n-1 + Á + a1x + a0
A matrix A = [aij] with the property aij = aji for all i and j
A circle with radius 1 centered at the origin.
The directed distance from the x-axis xz-plane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.