- 8.1: Newtons Law of Cooling Suppose that an object has temperature T and...
- 8.2: In this problem, we discuss a model for clonal growth in the white ...
- 8.3: Diversification of Life Several models have been proposed to explai...
- 8.4: A Simple Model for Photosynthesis of Individual Leaves Photosynthes...
- 8.5: Gompertz Growth Model This model is sometimes used to study the gro...
- 8.6: Island Biogeography Preston (1962) and MacArthur and Wilson (1963) ...
- 8.7: Chemostat A chemostat is an apparatus for growing bacteria in a med...
- 8.8: In Subsection 8.3.3, we introduced a hierarchical competition model...
Solutions for Chapter 8: Review Problems
Full solutions for Calculus For Biology and Medicine (Calculus for Life Sciences Series) | 3rd Edition
An observational study that gathers data from an entire population
Chord of a conic
A line segment with endpoints on the conic
A circular graphical display of categorical data
A measure of the strength of the linear relationship between two variables, pp. 146, 162.
The process of utilizing general information to prove a specific hypothesis
Difference of two vectors
<u1, u2> - <v1, v2> = <u1 - v1, u2 - v2> or <u1, u2, u3> - <v1, v2, v3> = <u1 - v1, u2 - v2, u3 - v3>
The line through the focus and perpendicular to the directrix of a conic.
Graph of parametric equations
The set of all points in the coordinate plane corresponding to the ordered pairs determined by the parametric equations.
Notation used to specify intervals, pp. 4, 5.
Law of cosines
a2 = b2 + c2 - 2bc cos A, b2 = a2 + c2 - 2ac cos B, c2 = a2 + b2 - 2ab cos C
The graph of ƒ(x) = e-x2/2
Parallelogram representation of vector addition
Geometric representation of vector addition using the parallelogram determined by the position vectors.
See Parametric equations.
A set of parametric equations for a curve.
Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.
See Division algorithm for polynomials.
A function that can be written in the form f(x) = a sin (b (x - h)) + k or f(x) = a cos (b(x - h)) + k. The number a is the amplitude, and the number h is the phase shift.
Stretch of factor c
A transformation of a graph obtained by multiplying all the x-coordinates (horizontal stretch) by the constant 1/c, or all of the y-coordinates (vertical stretch) of the points by a constant c, c, > 1.
Terms of a sequence
The range elements of a sequence.
Zero of a function
A value in the domain of a function that makes the function value zero.