Math 1100
6
Midterm 3
April 11, 2007
NAME:
.
UID:
.
Importance:
steps of how
For each problem, you must show the
you get the nal answer to get credits.
Make sure your handwriting is readable.
GOOD LUCK!
1.
- (15pts) - Choose ONE of the two following questions to
Problem 1
answer
(a) Find
dy
dx
if y = log6 (x2 + 5x).
(b) Evaluate
tion.
R
p
2x3 + 5 2x2 dx. Then, check your result by dierentia-
1
2.
- (15pts) - Choose ONE of the two following questions to
answer. (HINT: Implicit dierentiation)
dy
(a) Find dx
if xe2y = 100y .
Problem 2
(b) Find
dy
dx
if ln(xy )
10x = 5 .
2
3.
Problem 3 - (20
x
2
ye
y
3x =
pts) - Write the equation of the tangent line to the curve
2 at (0; 2). (HINT: Implicit dierentiation)
3
4.
Problem 4
do.
- (20 pts) - Choose ONE of the following problems A or B to
A - Elasticity
Suppose that the demand for a product is given by 2pq + 10p = 100.
(a) Find the elasticity when p = $5, q = 5. (HINT: Find dq=dp rst)
(b) Tell what type of elasticity this is : unitary, elastic, or inelastic.
(c) How would revenue be aected by a price increase?
4
B - Taxes
If the weekly demand function is p = 100 2q and the supply function
before taxation is p = 40 + 3q , what tax per item will maximize the total
tax revenue?
5
5.
- (30 pts) - The function and its rst and second derivatives
are given. Use these to nd any horizontal and vertical asymptotes, critical points, relative maxima, relative minima, and point of inection. Then
sketch the graph of the function.
Problem 5
y
0
=
00
=
y
y
=
6
2)2
(x
x
2
4(x
3
x
8(x
4
x
2)
3)