Recitations 28, 29 MA113:004{006
1, 3 December 1998 Fall 1998
Below is a selection of problems related to section 4.5, L'hopital's rule and 4.6,
optimization problems. These problems will not be collected or graded. However,
you should understand howtowork each of these problems. You should begin
working on these problems in groups in recitation. You will probably want to nish
these problems outside of class. If you have questions, please ask your TAor
instructor. If you nd a problem dicult, consider working similar problems from
the text for additional practice.
Announcements: 1. The nal for this course is in CB122 (note room change!) from
8:30{10:30 on Monday, 14 December 1998. 2. The last project is due on 4 December
1998.
1. Written homework due at 10am on 7 December 1998.
x
4.5 14, 48.
x
4.6 10, 30.
2. Section 4.5 #1, 3, 5, 7, 9, 13, 15, 43, 47.
3. Section 4.6 #1, 3, 9, 11, 17, 21, 31.
4. Find two functions
f
and
g
where
lim
x
!
0
f
(
x
)
g
(
x
)
=7 and lim
x
!
0
f
0
(
x
)
g
0
(
x
)
=3
:
Can you replace 3 and 7 byanynumbers
a
and
b
?
5. (Review) Dierentiate
e
,
3
x
2
and
p
1
,
sin
2
x
.
6. (Review) Suppose that the two shortest sides of a right triangle
a
(
t
) and
b
(
t
)
vary with time and after
t
seconds
a
(
t
)=
t
2
meters and
b
(
t
)=
t
meters.
(a) Let
c
(
t
) b e the hypotenuse and nd
c
0
(
t
).
(b) Let
be the angle opposite the side whose length is
b
(
t
) and nd
0
(2).
(c) Whyis
0
(
t
)=
,
0
(
t
)? Here,
denotes the angle opposite the side whose
length is
a
(
t
).
November 25, 1998
