- 7.1.1: Show that is a solution of the differential equation .
- 7.1.2: Verify that is a solution of the initial-value problem t dy dt y t2...
- 7.1.3: (a) For what values of does the function satisfy the differential e...
- 7.1.4: (a) For what values of does the function satisfy the differential e...
- 7.1.5: Which of the following functions are solutions of the differential ...
- 7.1.6: (a) Show that every member of the family of functions is a solution...
- 7.1.7: (a) What can you say about a solution of the equation just by looki...
- 7.1.8: (a) What can you say about the graph of a solution of the equation ...
- 7.1.9: A population is modeled by the differential equationdP dt 1.2P1 P 4...
- 7.1.10: A function satises the differential equationdy dt y4 6y3 5y2(a) Wha...
- 7.1.11: Explain why the functions with the given graphs cant be solutions o...
- 7.1.12: The function with the given graph is a solution of one of the follo...
- 7.1.13: Match the differential equations with the solution graphs labeled I...
- 7.1.14: Suppose you have just poured a cup of freshly brewed coffee with te...
- 7.1.15: Psychologists interested in learning theory study learning curves. ...
Solutions for Chapter 7.1: MODELING WITH DIFFERENTIAL EQUATIONS
Full solutions for Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) | 4th Edition
A value ƒ(c) is an absolute minimum value of ƒ if ƒ(c) ? ƒ(x)for all x in the domain of ƒ.
Absolute value of a complex number
The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.
See Inverse tangent function.
A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined
Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)
See Polar coordinates.
Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2
A method of solving a system of linear equations
A function whose graph is symmetric about the y-axis for all x in the domain of ƒ.
The right side of u(v + w) = uv + uw.
The terms of the Fibonacci sequence.
A series whose terms form a geometric sequence.
See Component form of a vector.
Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.
Inverse tangent function
The function y = tan-1 x
Permutations of n objects taken r at a time
There are nPr = n!1n - r2! such permutations
The formula x = -b 2b2 - 4ac2a used to solve ax 2 + bx + c = 0.
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.
Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt
Vertex of a parabola
The point of intersection of a parabola and its line of symmetry.