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Free Response Final 2006
Name
1. Consider the differential equation
dy
ccccccc
dx
=
2x
ccccccc
y
H
A
L
On the axes provided below, sketch a slope field for the given differential equation at the 15
points indicated, and sketch the solution curve that passes through the point
H
0, 2
L
.
1
2
2
3
4
5
H
B
L
Using the differential equation above,
dy
ccccccc
dx
=
2x
cccccccc
y
, and Euler
±
s method starting at f
H
0
L
=
2, and a
step size
H
∆
x
L
of 1,
calculate f
H
2
LH
take two steps
L
.
H
C
L
Now, solve the differential equation
dy
ccccccc
dx
=
2x
cccccccc
y
where
y
H
0
L
=
2. What type of curve is this?

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*Sign up* 2. Wow, it
±
s getting cold all of a sudden
!
Below is a table of temperatures taken outside the Monta Vista
main office on Monday morning.
Time
H
t
L
6 am
7 am
8 am
9 am
10 am
11 am
12 pm
Temperature
H
in degrees Celsius
L
3
7
10
12
14
15
16
H
A
L
If we assume that the temperature during the 6 hour period can be modeled by a differentiable function
W
H
t
L
, approximate W
±
H
8
L
, and indicate units of measure.
H

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