- 9.1.1: Show that is a solution of the differential equation
- 9.1.2: Verify that is a solution of the initial-value problem tdydt y t2 s...
- 9.1.3: (a) For what values of does the function satisfy the differential e...
- 9.1.4: (a) For what values of does the function satisfy the differential e...
- 9.1.5: Which of the following functions are solutions of the differential ...
- 9.1.6: (a) Show that every member of the family of functions is a solution...
- 9.1.7: (a) What can you say about a solution of the equation just by looki...
- 9.1.8: (a) What can you say about the graph of a solution of the equation ...
- 9.1.9: A population is modeled by the differential equation (a) For what v...
- 9.1.10: A function satisfies the differential equation (a) What are the con...
- 9.1.11: Explain why the functions with the given graphs cant be solutions o...
- 9.1.12: The function with the given graph is a solution of one of the follo...
- 9.1.13: Match the differential equations with the solution graphs labeled I...
- 9.1.14: Suppose you have just poured a cup of freshly brewed coffee with te...
- 9.1.15: Psychologists interested in learning theory study learning curves. ...
Solutions for Chapter 9.1: Modeling with Differential Equations
Full solutions for Calculus: Early Transcendentals | 7th Edition
An angle whose vertex is the center of a circle
Constant function (on an interval)
ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)
An identity involving a trigonometric function of u - v
Directed line segment
Any solution of the resulting equation that is not a solution of the original equation.
The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.
The complex number.
A special case of a limit that does not exist.
See Natural logarithmic regression
Magnitude of a vector
The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2
Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012 - ƒ1a - 0.00120.002
Real numbers shown to the right of the origin on a number line.
Projection of u onto v
The vector projv u = au # vƒvƒb2v
See Power function
A variable (in statistics) that takes on numerical values for a characteristic being measured.
Reflection across the y-axis
x, y and (-x,y) are reflections of each other across the y-axis.
A matrix whose number of rows equals the number of columns.
Standard representation of a vector
A representative arrow with its initial point at the origin
A vector that specifies the motion of an object in terms of its speed and direction.
A procedure of a graphing utility used to view more of the coordinate plane (used, for example, to find theend behavior of a function).