Victor Camocho
WeBWorK assignment number Homework 4 is due : 09/15/2011 at 11:00pm MDT.
The
(* replace with url for the course home page *) for the course contains the syllabus, grading policy and other information.
math2250fall2011-2
This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.
The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor for help. Don’t spend a lot of time guessing – it’s not very efficient or effective.
Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 ∧ 3 instead of 8, sin ( 3 ∗ pi / 2 ) instead of -1, e ∧ ( ln ( 2 )) instead of 2,
( 2 + tan ( 3 )) ∗ ( 4 − sin ( 5 )) ∧ 6 − 7 / 8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.
You can use the Feedback button on each problem page to send e-mail to the professors.
1.
(1 pt) Library/Michigan/Chap11Sec3/Q05.pg
Consider the differential equation dy dx
= 7 x , with initial condition y ( 0 ) = 2.
A.
Use Euler’s method with two steps to estimate y when x = 1: y ( 1 ) ≈
(Be sure not to round your calculations at each step!)
Now use four steps: y ( 1 ) ≈
(Be sure not to round your calculations at each step!)
B.
What is the solution to this differential equation (with the given initial condition)?
y =
C.
What is the magnitude of the error in the two Euler approximations you found?
Magnitude of error in Euler with 2 steps =
Magnitude of error in Euler with 4 steps =
D.
By what factor should the error in these approximations change (that is, the error with two steps should be what number times the error with four)?
factor =
(How close to this is the result you obtained above?) y ( 2
2.
(1 pt) Library/Rochester/setDiffEQ2DirectionFields/ur de 2 6.pg
Use Euler’s method with step size 0 .
4 to estimate y ( 2 ) , where y ( x ) is the solution of the initial-value problem
) = .
y
0
= − 3 x + y
2
, y ( 0 ) = − 1 .
3.
(1 pt) Library/Rochester/setDiffEQ2DirectionFields/ur de 2 5.pg
Use Euler’s method with step size 0 mate y -values y
1
, y
2
, y
3
, and y
4 problem y y
2
= y y
1
3
4
=
=
=
,
,
,
.
y
0
= − 1 + 3 x
.
25 to compute the approxiof the solution of the initial-value
+ 4 y , y ( 1 ) =
4.
(1 pt) Library/Michigan/Chap11Sec3/Q03.pg
4 .
Consider the solution of the differential equation y
0 ing through y ( 0 ) = 1 .
5.
solution at table.
x =
(Be sure
0 .
2 not
, 0 .
4 , . . . ,
= − to round your answers at each step!)
4 y pass-
A.
Sketch the slope field for this differential equation, and sketch the solution passing throughthe point (0,1.5).
B.
Use Euler’s method with step size
∆ x = 0 .
2 to estimate the
1, using these to fill in the following
1 x = 0 0.2
0.4
0.6
0.8
1.0
y ≈ 1.5
C.
Plot your estimated solution on your slope field. Compare the solution and the slope field. Is the estimated solution an over or under estimate for the actual solution?
• A. over
• B. under
D.
Check that y = 1 .
5 e
− 4 x y ( 0 ) = 1 .
5.
is a solution to y
0
= − 4 y with
5.
(1 pt) Library/maCalcDB/setLinearAlgebra1Systems/ur la 1 4a.pg
Solve the system using elimination
− 2 x + 9 y = − 18
3 x + 3 y = − 39

x = y =
6.
(1 pt) Library/maCalcDB/setLinearAlgebra1Systems/ur la 1 5.pg
Solve the system using elimination
Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester x = y = z =



2 x − 5 y + 5 z = − 17
3 x − 6 y − 4 z = − 8
− 4 x + 5 y − 2 z = 6
2