 9.1.1: Show that is a solution of the differential equation
 9.1.2: Verify that is a solution of the initialvalue 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
ISBN: 9780538497909
Solutions for Chapter 9.1: Modeling with Differential Equations
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780538497909. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 7. Chapter 9.1: Modeling with Differential Equations includes 15 full stepbystep solutions. Since 15 problems in chapter 9.1: Modeling with Differential Equations have been answered, more than 31287 students have viewed full stepbystep solutions from this chapter.

Central angle
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)

Difference identity
An identity involving a trigonometric function of u  v

Directed line segment
See Arrow.

Extraneous solution
Any solution of the resulting equation that is not a solution of the original equation.

Halfplane
The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.

Imaginary unit
The complex number.

Infinite limit
A special case of a limit that does not exist.

Logarithmic regression
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

Positive numbers
Real numbers shown to the right of the origin on a number line.

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Proportional
See Power function

Quantitative variable
A variable (in statistics) that takes on numerical values for a characteristic being measured.

Reflection across the yaxis
x, y and (x,y) are reflections of each other across the yaxis.

Square matrix
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

Velocity
A vector that specifies the motion of an object in terms of its speed and direction.

Zoom out
A procedure of a graphing utility used to view more of the coordinate plane (used, for example, to find theend behavior of a function).