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.
Problem 1
answer
(a) Find
dy
dx
(b) Evaluate
- (10pts) - Choose ONE of the two following questions to
if y = log3 (x2
R
p
x
3
2x).
5 2x2 dx. Then, check your result by dierentiation.
1
2.
- (15pts) - Choose ONE of the two following questions to
answer. (HINT: Implicit dierentiation)
dy
(a) Find dx
if e2y 5x = 100.
Problem 2
(b) Find
dy
dx
if ln(xy ) = y .
2
3.
Problem 3
2
xy + y = 0
- (15 pts) - Write the equation of the tangent line to the curve
at (3; 0). (HINT: Implicit dierentiation)
3
4.
Problem 4
do.
- (15 pts) - Choose ONE of the following problems A or B to
A - Elasticity
Suppose that the demand for a product is given by p2 q 2 + 2p = 20.
(a) Find the elasticity when p = $2, q = 2. (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 = 32 q and the supply function before taxation is p = 4 + q , 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
y
y
0
00
=
x
(x + 1)2
1 x
=
(x + 1)3
2x 4
=
(x + 1)4
6