- 9.5.1E: List three important considerations that are ignored in the competi...
- 9.5.2E: For the system (2a) and (2b), show that any trajectory starting on ...
- 9.5.3E: Develop a model for the growth of trout and bass, assuming that in ...
- 9.5.4E: How might the competitive-hunter model be validated? Include a disc...
- 9.5.5E: Consider another competitive-hunter model defined by where x and y ...
- 9.5.6E: An economic model Consider the following economic model. Let P be t...
- 9.5.7E: Two trajectories approach equilibrium Show that the two trajectorie...
- 9.5.8E: Show that the second-order differential equation can be reduced to ...
- 9.5.9E: Lotka-Volterra Equations for a Predator-Prey ModelIn 1925 Lotka and...
- 9.5.10E: Lotka-Volterra Equations for a Predator-Prey ModelIn 1925 Lotka and...
- 9.5.11E: Lotka-Volterra Equations for a Predator-Prey ModelIn 1925 Lotka and...
- 9.5.12E: Lotka-Volterra Equations for a Predator-Prey ModelIn 1925 Lotka and...
- 9.5.13E: Using a procedure similar to that in the text for the competitivehu...
- 9.5.14E: At some time during a trajectory cycle, a wolf invades the rabbit-f...
Solutions for Chapter 9.5: Thomas' Calculus: Early Transcendentals 13th Edition
Full solutions for Thomas' Calculus: Early Transcendentals | 13th Edition
The graph of the parametric equations
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists
Direction vector for a line
A vector in the direction of a line in three-dimensional space
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment
Elementary row operations
The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row
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.
Inverse cosine function
The function y = cos-1 x
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.
See Polar coordinate system.
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.
Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,
Product of functions
(ƒg)(x) = ƒ(x)g(x)
A plot of all the ordered pairs of a two-variable data set on a coordinate plane.
A finite or infinite sum of terms.
Terms of a sequence
The range elements of a sequence.
The line x = a is a vertical asymptote of the graph of the function ƒ if limx:a+ ƒ1x2 = q or lim x:a- ƒ1x2 = q.
A shift of a graph up or down.
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.
The directed distance from the xy-plane to a point in space, or the third number in an ordered triple.
Zero factor property
If ab = 0 , then either a = 0 or b = 0.