- 7-6.Q1: f(x) dx = f(c) x is a brief statement of
- 7-6.Q2: f(x) dx = g(b) g(a) is a brief statement of
- 7-6.Q3: f(x) dx = g(x) if and only if f(x) = (x) is a statement of the ?.
- 7-6.Q4: . . . then there is a point c in (a, b) such that f(c) = k is the c...
- 7-6.Q5: . . . then there is a point c in (a, b) such that (c) = 0 is the co...
- 7-6.Q6: . . . then there is a point c in (a, b) such that is the conclusion...
- 7-6.Q7: . . . then (x) = (h(x)) (x) is the conclusion of ?.
- 7-6.Q8: f(x) = cos x + C is the ? solution of a differential equation
- 7-6.Q9: f(x) = cos x + 5 is a(n) ? solution of a differential equation
- 7-6.Q10: f(0) = 6 is a(n) ? condition for the differential equation in Q9
- 7-6.1: Bacteria Problem: Harry and Hermione start a culture of bacteria in...
- 7-6.2: Subdivision Building Problem: A real estate developer opens up a sm...
- 7-6.3: Merchandise Sales Problem: When a new product is brought onto the m...
- 7-6.4: General Solution of the Logistic Differential Equation: Start with ...
- 7-6.5: Snail Darter Endangered Species Problem: The snail darter is a smal...
- 7-6.6: Rumor-Spreading Experiment: Number off the members of your class. P...
- 7-6.7: U.S. Population Project: The following table shows the U.S. populat...
- 7-6.8: Algebraic Solution of the Logistic Equation: As you have seen, it i...
- 7-6.9: Let R be the number of rabbits, in hundreds, and F be the number of...
- 7-6.10: If there are no rabbits for the foxes to eat, the fox population de...
- 7-6.11: Assume that the foxes eat rabbits at a rate proportional to the num...
- 7-6.12: Use the chain rule to write a differential equation for dF/dR. What...
- 7-6.13: Assume that the four constants in the differential equation are suc...
- 7-6.14: Figure 7-6g shows the slope field for this differential equation. O...
- 7-6.15: How would you describe the behavior of the rabbit and fox populations?
- 7-6.16: Is there a fixed point at which both the rabbit and the fox populat...
- 7-6.17: The logistic equation of shows that, because of overcrowding, the r...
- 7-6.18: The slope field in Figure 7-6h is for dF/dR, which you calculated i...
- 7-6.19: How does the graph in differ from that in 14? How does overcrowding...
- 7-6.20: Ona tries to reduce the rabbit population by allowing hunters to co...
- 7-6.21: The slope field in Figure 7-6i is for the differential equation On ...
- 7-6.22: Describe what happens to the populations of rabbits and foxes under...
- 7-6.23: Worried about the fate of the foxes in 21, Ona imports 15 more of t...
Solutions for Chapter 7-6: The Logistic Function, and Predator-Prey Population Problems
Full solutions for Calculus: Concepts and Applications | 2nd Edition
Solutions for Chapter 7-6: The Logistic Function, and Predator-Prey Population ProblemsGet Full Solutions
Convergence of a series
A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S
The process of utilizing general information to prove a specific hypothesis
An identity involving a trigonometric function of u - v
Difference of complex numbers
(a + bi) - (c + di) = (a - c) + (b - d)i
For the equation ax 2 + bx + c, the expression b2 - 4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2 - 4AC
A set with no elements
The right side of u(v + w) = uv + uw.
Focal width of a parabola
The length of the chord through the focus and perpendicular to the axis.
The amount of time required for half of a radioactive substance to decay.
Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x:- q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large
An expression of the form logb x (see Logarithmic function)
Magnitude of a vector
The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2
Paraboloid of revolution
A surface generated by rotating a parabola about its line of symmetry.
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.
Sum of a finite arithmetic series
Sn = na a1 + a2 2 b = n 2 32a1 + 1n - 12d4,
The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series
symmetric about the x-axis
A graph in which (x, -y) is on the graph whenever (x, y) is; or a graph in which (r, -?) or (-r, ?, -?) is on the graph whenever (r, ?) is
A visualization of the relationships among events within a sample space.
Zero of a function
A value in the domain of a function that makes the function value zero.