 7.6.1E: ?In 1–4, sketch the graph of the given function and determine its L...
 7.6.2E: ?In 1–4, sketch the graph of the given function and determine its L...
 7.6.3E: In 1–4, sketch the graph of the given function and determine its La...
 7.6.4E: ?In 1–4, sketch the graph of the given function and determine its L...
 7.6.5E: In 5–10, express the given function using window and step functions...
 7.6.6E: In 5–10, express the given function using window and step functions...
 7.6.7E: ?In 5–10, express the given function using window and step function...
 7.6.8E: ?In 5–10, express the given function using window and step function...
 7.6.9E: ?In 5–10, express the given function using window and step function...
 7.6.10E: ?In 5–10, express the given function using window and step function...
 7.6.11E: ?In 11–18, determine an inverse Laplace transform of the given func...
 7.6.12E: ?In 11–18, determine an inverse Laplace transform of the given func...
 7.6.13E: ?In 11–18, determine an inverse Laplace transform of the given func...
 7.6.14E: ?In 11–18, determine an inverse Laplace transform of the given func...
 7.6.15E: In 11–18, determine an inverse Laplace transform of the given funct...
 7.6.16E: In 11–18, determine an inverse Laplace transform of the given funct...
 7.6.17E: ?In 11–18, determine an inverse Laplace transform of the given func...
 7.6.18E: In 11–18, determine an inverse Laplace transform of the given funct...
 7.6.19E: ?The current in an RLC series circuit is governed by the initial va...
 7.6.20E: ?The current in an LC series circuit is governed by the initial val...
 7.6.21E: ?In 21–24, determine , where is periodic with the given period. Als...
 7.6.22E: ?In 21–24, determine , where is periodic with the given period. Als...
 7.6.23E: ?In 2124, determine , where is periodic with the given period. Als...
 7.6.24E: ?In 21–24, determine , where is periodic with the given period. Als...
 7.6.25E: In 25–28, determine where the periodic function is described by its...
 7.6.26E: In 25–28, determine where the periodic function is described by its...
 7.6.27E: ?In 25–28, determine , where the periodic function is described by ...
 7.6.28E: In 25–28, determine where the periodic function is described by its...
 7.6.29E: ?In 29–32, solve the given initial value problem using the method o...
 7.6.30E: ?In 29–32, solve the given initial value problem using the method o...
 7.6.31E: ?In 29–32, solve the given initial value problem using the method o...
 7.6.32E: In 29–32, solve the given initial value problem using the method of...
 7.6.33E: ?In 33–40, solve the given initial value problem using the method o...
 7.6.34E: ?In 33–40, solve the given initial value problem using the method o...
 7.6.35E: ?In 33–40, solve the given initial value problem using the method o...
 7.6.36E: ?In 33–40, solve the given initial value problem using the method o...
 7.6.37E: In 33–40, solve the given initial value problem using the method of...
 7.6.38E: In 33–40, solve the given initial value problem using the method of...
 7.6.39E: In 33–40, solve the given initial value problem using the method of...
 7.6.40E: In 33–40, solve the given initial value problem using the method of...
 7.6.41E: ?Show that if , where is fixed, then(21) [Hint: Use the fact that
 7.6.42E: ?The function g(t) in (21) can be expressed in a moreconvenient for...
 7.6.43E: ?Show that if , then
 7.6.44E: ?44. Use the result of to show that In 45 and 46, use the method of...
 7.6.45E: In 45 and 46, use the method of Laplace transforms and the results ...
 7.6.46E: In 45 and 46, use the method of Laplace transforms and the results ...
 7.6.47E: ?In , find a Taylor series for about Assuming the Laplace transform...
 7.6.48E: In 47–50, find a Taylor series for f(t) about t=0. Assuming the Lap...
 7.6.49E: ?In , find a Taylor series for about Assuming the Laplace transform...
 7.6.50E: In 47–50, find a Taylor series for f(t) about t=0. Assuming the Lap...
 7.6.51E: ?51. Using the recursive relation (19) and the fact that
 7.6.52E: ?52. Use the recursive relation (19) and the fact that
 7.6.53E: Verify (15) in Theorem 9 for the function f(t) = sin t, taking the ...
 7.6.54E: By replacing s (1/s) by in the Maclaurin series expansion for arcta...
 7.6.55E: Find an expansion for e1/s in powers of 1/s. Use the expansion for...
 7.6.56E: Use the procedure discussed in to show that. Find an expansion for ...
 7.6.57E: ?Find an expansion for ln[1 + (1/s2)] in powers of 1/s. Assuming th...
Solutions for Chapter 7.6: Fundamentals of Differential Equations 8th Edition
Full solutions for Fundamentals of Differential Equations  8th Edition
ISBN: 9780321747730
Solutions for Chapter 7.6
Get Full SolutionsFundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. Chapter 7.6 includes 57 full stepbystep solutions. Since 57 problems in chapter 7.6 have been answered, more than 159805 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. This expansive textbook survival guide covers the following chapters and their solutions.

Binomial theorem
A theorem that gives an expansion formula for (a + b)n

Compounded annually
See Compounded k times per year.

Dihedral angle
An angle formed by two intersecting planes,

Distance (in a coordinate plane)
The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1  x 2)2 + (y1  y2)2

Fitting a line or curve to data
Finding a line or curve that comes close to passing through all the points in a scatter plot.

Gaussian curve
See Normal curve.

Integrable over [a, b] Lba
ƒ1x2 dx exists.

Leading term
See Polynomial function in x.

Major axis
The line segment through the foci of an ellipse with endpoints on the ellipse

Matrix element
Any of the real numbers in a matrix

Mean (of a set of data)
The sum of all the data divided by the total number of items

Multiplicity
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x  c) (x  z 2) Á (x  z n)

NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx

Odd function
A function whose graph is symmetric about the origin (ƒ(x) = ƒ(x) for all x in the domain of f).

Parameter
See Parametric equations.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Real zeros
Zeros of a function that are real numbers.

Root of an equation
A solution.

Spiral of Archimedes
The graph of the polar curve.

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>