- 6.1: Discharge of a River In studying the flow of water in an open chann...
- 6.2: Biomass Growth Suppose that you grow plants in several study plots ...
- 6.3: (a) Sketch the graph of v(d) as a function of d for D = 3 m and a =...
- 6.4: (a) Show by integration that the average speed v in the vertical pr...
- 6.5: Explain why the depth d1, at which v = v, is given by the equation ...
- 6.6: We denote by v0.2 the speed at depth 0.2D. We will now find the dep...
Solutions for Chapter 6: Review Problems
Full solutions for Calculus For Biology and Medicine (Calculus for Life Sciences Series) | 3rd Edition
Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data
Convergence of a series
A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S
Coordinate(s) of a point
The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian three-dimensional space
A nonnegative number that specifies how off-center the focus of a conic is
A set with no elements
The behavior of a graph of a function as.
equation of a parabola
(x - h)2 = 4p(y - k) or (y - k)2 = 4p(x - h)
Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).
Grapher or graphing utility
Graphing calculator or a computer with graphing software.
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
A graph of data in which consecutive data points are connected by line segments
Linear regression equation
Equation of a linear regression line
Logarithmic re-expression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression
Lower bound of f
Any number b for which b < ƒ(x) for all x in the domain of ƒ
Equations of the form x = ƒ(t) and y = g(t) for all t in an interval I. The variable t is the parameter and I is the parameter interval.
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.
Probability of an event in a finite sample space of equally likely outcomes
The number of outcomes in the event divided by the number of outcomes in the sample space.