Calculus:Early...-Webassign Access
8th Edition
ISBN: 9781337771474
Author: Stewart
Publisher: Cengage
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Chapter 17.3, Problem 1E
A spring has natural length 0.75 m and a 5-kg mass. A force of 25 N is needed to keep the spring stretched to a length of 1 m. If the spring is stretched to a length of 1.1 m and then released with velocity 0, find the position of the mass after t seconds.
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A function is defined on the interval (-π/2,π/2) by this multipart rule:
if -π/2 < x < 0
f(x) =
a
if x=0
31-tan x
+31-cot x
if 0 < x < π/2
Here, a and b are constants. Find a and b so that the function f(x) is continuous at x=0.
a=
b= 3
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
f(x) = (x + 4x4) 5,
a = -1
lim f(x)
X--1
=
lim
x+4x
X--1
lim
X-1
4
x+4x
5
))"
5
))
by the power law
by the sum law
lim (x) + lim
X--1
4
4x
X-1
-(0,00+(
Find f(-1).
f(-1)=243
lim (x) +
-1 +4
35
4 ([
)
lim (x4)
5
x-1
Thus, by the definition of continuity, f is continuous at a = -1.
by the multiple constant law
by the direct substitution property
1. Compute
Lo
F⚫dr, where
and C is defined by
F(x, y) = (x² + y)i + (y − x)j
r(t) = (12t)i + (1 − 4t + 4t²)j
from the point (1, 1) to the origin.
Chapter 17 Solutions
Calculus:Early...-Webassign Access
Ch. 17.1 - Solve the differential equation. 1. y" y' 6y = 0Ch. 17.1 - Solve the differential equation. 2. y" 6y' + 9y =...Ch. 17.1 - Solve the differential equation. 3. y" + 2y = 0Ch. 17.1 - Solve the differential equation. 4. y" + y' 12y =...Ch. 17.1 - Solve the differential equation. 5. 4y" + 4y' + y...Ch. 17.1 - Solve the differential equation. 6. 9y" + 4y = 0Ch. 17.1 - Solve the differential equation. 7. 3y" = 4y'Ch. 17.1 - Prob. 8ECh. 17.1 - Solve the differential equation. 9. y" 4y' + 13y...Ch. 17.1 - Prob. 10E
Ch. 17.1 - Solve the differential equation. 11....Ch. 17.1 - Prob. 12ECh. 17.1 - Prob. 13ECh. 17.1 - Prob. 14ECh. 17.1 - Prob. 15ECh. 17.1 - Prob. 16ECh. 17.1 - Prob. 17ECh. 17.1 - Prob. 18ECh. 17.1 - Prob. 19ECh. 17.1 - Prob. 20ECh. 17.1 - Solve the initial-value problem. 21. y" 6y' + 10y...Ch. 17.1 - Solve the initial-value problem. 22. 4y" 20y' +...Ch. 17.1 - Prob. 23ECh. 17.1 - Solve the initial-value problem. 24. 4y" + 4y' +...Ch. 17.1 - Solve the boundary-value problem, if possible. 25....Ch. 17.1 - Prob. 26ECh. 17.1 - Prob. 27ECh. 17.1 - Prob. 28ECh. 17.1 - Solve the boundary-value problem, if possible. 29....Ch. 17.1 - Prob. 30ECh. 17.1 - Prob. 31ECh. 17.1 - Prob. 32ECh. 17.1 - Prob. 33ECh. 17.1 - If a, b, and c are all positive constants and y(x)...Ch. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Prob. 2ECh. 17.2 - Prob. 3ECh. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Prob. 5ECh. 17.2 - Prob. 6ECh. 17.2 - Prob. 7ECh. 17.2 - Prob. 8ECh. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Prob. 10ECh. 17.2 - Prob. 11ECh. 17.2 - Prob. 12ECh. 17.2 - Write a trial solution for the method of...Ch. 17.2 - Prob. 14ECh. 17.2 - Prob. 15ECh. 17.2 - Prob. 16ECh. 17.2 - Prob. 17ECh. 17.2 - Write a trial solution for the method of...Ch. 17.2 - Solve the differential equation using (a)...Ch. 17.2 - Prob. 20ECh. 17.2 - Solve the differential equation using (a)...Ch. 17.2 - Prob. 22ECh. 17.2 - Prob. 23ECh. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Prob. 25ECh. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Solve the differential equation using the method...Ch. 17.3 - A spring has natural length 0.75 m and a 5-kg...Ch. 17.3 - A spring with an 8-kg mass is kept stretched 0.4 m...Ch. 17.3 - A spring with a mass of 2 kg has damping constant...Ch. 17.3 - Prob. 4ECh. 17.3 - For the spring in Exercise 3, find the mass that...Ch. 17.3 - Prob. 6ECh. 17.3 - Prob. 7ECh. 17.3 - Prob. 8ECh. 17.3 - Suppose a spring has mass m and spring constant k...Ch. 17.3 - As in Exercise 9, consider a spring with mass m,...Ch. 17.3 - Prob. 11ECh. 17.3 - Prob. 12ECh. 17.3 - A series circuit consists of a resistor with R =...Ch. 17.3 - A series circuit contains a resistor with R = 24 ,...Ch. 17.3 - The battery in Exercise 13 is replaced by a...Ch. 17.3 - Prob. 16ECh. 17.3 - Prob. 17ECh. 17.3 - The figure shows a pendulum with length I, and the...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Prob. 2ECh. 17.4 - Prob. 3ECh. 17.4 - Prob. 4ECh. 17.4 - Prob. 5ECh. 17.4 - Prob. 6ECh. 17.4 - Prob. 7ECh. 17.4 - Prob. 8ECh. 17.4 - Prob. 9ECh. 17.4 - Prob. 10ECh. 17.4 - Prob. 11ECh. 17.4 - The solution of the initial-value problem x2y" +...Ch. 17 - (a) Write the general form of a second-order...Ch. 17 - (a) What is an initial-value problem for a...Ch. 17 - (a) Write the general form of a second-order...Ch. 17 - Prob. 4RCCCh. 17 - Prob. 5RCCCh. 17 - Prob. 1RQCh. 17 - Prob. 2RQCh. 17 - Prob. 3RQCh. 17 - Prob. 4RQCh. 17 - Prob. 1RECh. 17 - Prob. 2RECh. 17 - Prob. 3RECh. 17 - Prob. 4RECh. 17 - Prob. 5RECh. 17 - Prob. 6RECh. 17 - Prob. 7RECh. 17 - Prob. 8RECh. 17 - Prob. 9RECh. 17 - Prob. 10RECh. 17 - Prob. 11RECh. 17 - Solve the initial-value problem. 12. y" 6y' + 25y...Ch. 17 - Prob. 13RECh. 17 - Solve the initial-value problem. 14. 9y" + y =3x +...Ch. 17 - Prob. 15RECh. 17 - Prob. 16RECh. 17 - Use power series to solve the initial-value...Ch. 17 - Use power series to solve differential equation y"...Ch. 17 - Prob. 19RECh. 17 - A spring with a mass of 2 kg has damping constant...Ch. 17 - Assume that the earth is a solid sphere of uniform...
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