- 12.1: State the rules for differentiating and integrating vector function...
- 12.2: How do you define and calculate the velocity, speed, direction of m...
- 12.3: What is special about the derivatives of vector functions of con-st...
- 12.4: What are the vector and parametric equations for ideal projectile m...
- 12.5: How do you define and calculate the length of a segment of asmooth ...
- 12.6: How do you measure distance along a smooth curve in space from a pr...
- 12.7: What is a differentiable curves unit tangent vector? Give an example.
- 12.8: Define curvature, circle of curvature (osculating circle), center o...
- 12.9: What is a plane curves principal normal vector? When is it defined?...
- 12.10: How do you define N and k for curves in space?
- 12.11: What is a curves binormal vector? Give an example.
- 12.12: What formulas are available for writing a moving objects accel-erat...
- 12.13: State Keplers laws.
Solutions for Chapter 12: University Calculus: Early Transcendentals 3rd Edition
Full solutions for University Calculus: Early Transcendentals | 3rd Edition
The notation PQ denoting the directed line segment with initial point P and terminal point Q.
An interval that includes its endpoints
Completing the square
A method of adding a constant to an expression in order to form a perfect square
See Linear programming problem.
Derivative of ƒ
The function defined by ƒ'(x) = limh:0ƒ(x + h) - ƒ(x)h for all of x where the limit exists
equation of a parabola
(x - h)2 = 4p(y - k) or (y - k)2 = 4p(x - h)
Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.
A special case of a limit that does not exist.
Zeros of a function that are irrational numbers.
Linear inequality in x
An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0
A procedure for fitting a logistic curve to a set of data
Multiplication property of equality
If u = v and w = z, then uw = vz
Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.
NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx
Order of an m x n matrix
The order of an m x n matrix is m x n.
Reflection across the x-axis
x, y and (x,-y) are reflections of each other across the x-axis.
Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.
x = a.