MAT 1330, Fall 2010 Assignment 4
Due Wednesday November 10, at the beginning of class.
Late assignments will not be accepted; nor will unstapled assignments.
Instructor (circle one): Frithjof Lutscher
Angelika Welte
Aziz Khanchi
Robert Smith?
DGD (circle one): 1
2
3
4
Student Name
Student Number
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Question 1.
Find the derivatives of the following functions. Do not simplify.
a)
f
(
x
) = cos(
x
) sin(5
x
2
+ 7),
f
(
x
) =
b)
g
(
x
) =
tan(
x
)
e
7
x
x
4
,
g
(
x
) =
c)
h
(
x
) =
e
cos
3
x
+2 sin
2
x
,
h
(
x
) =
d)
w
(
y
) = ln(
y
2
+ 3
y
+ 9),
w
(
y
) =
e)
u
(
z
) =
sin(
z
5
)
√
z
,
u
(
z
) =
1
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Question 2.
Find the global minimum and the global maximum of
g
(
x
) = ln((
x
+ 1)
2
+ 1)
on the interval [
−
2
,
2].
Global maximum
at
x
=
.
Global minimum
at
x
=
.
Question 3.
The number of individuals (in thousands) of a certain species satisfies the
DTDS:
x
t
+1
=
5
x
t
1 +
x
t
−
hx
t
,
t
= 0
,
1
,
2
, . . .
The population is harvested according to a rate
h
≥
0.
Answer the following questions:
a)
The equilibrium points of this DTDS are (Hint: one of the equilibrium points will depend
on
h
):
and
.
b)
Give the largest interval for
h
such that both equilibrium points in (a) are nonnegative
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 Fall '08
 DUMITRISCU
 equilibrium points, Aziz Khanchi, Frithjof Lutscher, Angelika Welte, positive equilibrium

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