 9.1AAE: Theory and ApplicationsTransport through a cell membrane Under some...
 9.1PE: Solve the differential equation.
 9.1QGY: What is a firstorder differential equation? When is a function a s...
 9.2AAE: Theory and ApplicationsHeight of a rocket If an external force F ac...
 9.2PE: Solve the differential equation.
 9.2QGY: What is a general solution? A particular solution?
 9.3AAE: Theory and Applicationsa. Assume that P(x) and Q(x) are continuous ...
 9.3PE: Solve the differential equation.
 9.3QGY: What is the slope field of a differential equation y' = ƒ(x, y) ?Wh...
 9.4AAE: Theory and Applications(Continuation of Exercise 3.) Assume the hyp...
 9.4PE: Solve the differential equation.
 9.4QGY: Describe Euler’s method for solving the initial value problem numer...
 9.5AAE: Homogeneous EquationsA firstorder differential equation of the for...
 9.5PE: Solve the differential equation.
 9.5QGY: How do you solve linear firstorder differential equations?
 9.6AAE: Homogeneous EquationsA firstorder differential equation of the for...
 9.6PE: Solve the differential equation.
 9.6QGY: What is an orthogonal trajectory of a family of curves? Describe ho...
 9.7AAE: Homogeneous EquationsA firstorder differential equation of the for...
 9.7PE: Solve the differential equation.
 9.7QGY: What is an autonomous differential equation? What are its equilibri...
 9.8AAE: Homogeneous EquationsA firstorder differential equation of the for...
 9.8PE: Solve the differential equation.
 9.8QGY: How do you construct the phase line for an autonomous differential ...
 9.9AAE: Homogeneous EquationsA firstorder differential equation of the for...
 9.9PE: Solve the differential equation.
 9.9QGY: Why is the exponential model unrealistic for predicting longterm p...
 9.10AAE: Homogeneous EquationsA firstorder differential equation of the for...
 9.10PE: Solve the differential equation.
 9.10QGY: What is an autonomous system of differential equations? What is a s...
 9.11PE: Solve the differential equation.
 9.12PE: Solve the differential equation.
 9.13PE: Solve the differential equation.
 9.14PE: Solve the differential equation.
 9.15PE: Solve the differential equation.
 9.16PE: Solve the differential equation.
 9.17PE: Initial Value Solve the initial value problem.
 9.18PE: Initial Value Solve the initial value problem.
 9.19PE: Initial Value Solve the initial value problem.
 9.20PE: Initial Value Solve the initial value problem.
 9.21PE: Initial Value Solve the initial value problem.
 9.22PE: Initial Value Solve the initial value problem.
 9.23PE: Euler’s MethodUse Euler’s method to solve the initial value problem...
 9.24PE: Euler’s MethodUse Euler’s method to solve the initial value problem...
 9.25PE: Euler’s MethodUse Euler’s method with dx = 0.05 to estimate y(c) wh...
 9.26PE: Euler’s MethodUse Euler’s method with dx = 0.05 to estimate y(c) wh...
 9.27PE: Euler’s MethodUse Euler’s method to solve the initial value problem...
 9.28PE: Euler’s MethodUse Euler’s method to solve the initial value problem...
 9.29PE: Slope FieldsSketch part of the equation’s slope field. Then add to ...
 9.30PE: Slope FieldsSketch part of the equation’s slope field. Then add to ...
 9.31PE: Slope FieldsSketch part of the equation’s slope field. Then add to ...
 9.32PE: Slope FieldsSketch part of the equation’s slope field. Then add to ...
 9.33PE: Autonomous Differential Equations and Phase Linesa. Identify the eq...
 9.34PE: Autonomous Differential Equations and Phase Linesa. Identify the eq...
 9.35PE: ApplicationsEscape velocity The gravitational attraction F exerted ...
 9.36PE: ApplicationsCoasting to a stop Table 9.6 shows the distance s (mete...
Solutions for Chapter 9: Thomas' Calculus: Early Transcendentals 13th Edition
Full solutions for Thomas' Calculus: Early Transcendentals  13th Edition
ISBN: 9780321884077
Solutions for Chapter 9
Get Full SolutionsThis textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13. This expansive textbook survival guide covers the following chapters and their solutions. Since 56 problems in chapter 9 have been answered, more than 55359 students have viewed full stepbystep solutions from this chapter. Chapter 9 includes 56 full stepbystep solutions. Thomas' Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321884077.

Absolute minimum
A value ƒ(c) is an absolute minimum value of ƒ if ƒ(c) ? ƒ(x)for all x in the domain of ƒ.

Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal

Boxplot (or boxandwhisker plot)
A graph that displays a fivenumber summary

Components of a vector
See Component form of a vector.

Difference of complex numbers
(a + bi)  (c + di) = (a  c) + (b  d)i

Difference of functions
(ƒ  g)(x) = ƒ(x)  g(x)

First quartile
See Quartile.

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

General form (of a line)
Ax + By + C = 0, where A and B are not both zero.

Interval
Connected subset of the real number line with at least two points, p. 4.

Linear factorization theorem
A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1  z1) 1x  i z 22 Á 1x  z n where the z1 are the zeros of ƒ

Main diagonal
The diagonal from the top left to the bottom right of a square matrix

Matrix, m x n
A rectangular array of m rows and n columns of real numbers

Outliers
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

Principle of mathematical induction
A principle related to mathematical induction.

Rational function
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

Singular matrix
A square matrix with zero determinant

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

Trigonometric form of a complex number
r(cos ? + i sin ?)

Vertical asymptote
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.