FinalExamknation
Math 0120 Final Examination
Sample
Name (Print)
People Soft #
Signature
.
Instructor (circle one):
Lecture time (circle one):
Instructions:
1. Show your University of Pittsburgh ID if requested.
2. Clearly print your name and PeopleSoft n
Quiz 6
Math 0120
Spring 2013
Solutions
1. In a laboratory test the combined antibiotic eect of x milligrams of medicine A and y
milligrams of medicine B is given by the function
f (x, y ) = 2x2 + xy y 2 + 40x + 25y
(for 0 x 20, 0 y 25). Find the amounts o
Quiz 5
Math 0120
Spring 2013
Solutions
1. [5 points] Evaluate the integral
e
I=
4(ln x)3
dx
x
1
Solution:
1
Substitution: u = ln x, du = 4 dx, ln 1 = 0, ln e = 1. Then
e
1
1
4(ln x) dx =
x
3
I=
1
4u3 du = u4
1
=10=1
0
0
2. [5 points] Evaluate the integral
Quiz 4
Math 0120
Spring 2013
Solutions
1. For the demand function D(p) = 60 p p (a) [5 points] Find the elastisity of demand E (p).
Solution:
E ( p) =
D(p) = 60 p3/2 , D (p) = 3 p1/2
2
p ( 3 p1/2 )
p3/2
p D (p)
3
2
=
=
.
D(p)
60 p3/2
2 60 p3/2
(b) [5 poin
Quiz 3
Math 0120
Spring 2013
Solutions
1. [5 points] A farmer has 2000 ft of fencing and wants to fence o a rectangular eld that
borders a straight river. He needs no fence along the river. What are the dimensions (the
length L and width W) of the eld tha
Math 0120
Quiz 2
Spring 2013
Solutions
1. [5 points] For the function f (x) = 1 x2 nd f (x) by using the denition of the derivative
as a limit of its rate of change. No credit will be given if you do not use the denition.
Solution:
f (x) = lim
h0
f (x + h
Quiz 1
Spring 2013
Solutions
Math 0120
1. (a) [3 points] Find a slope-intercept form of a line that passes through the points (0, 3) and
(2, 7).
73
= 2. The point (0, 3) gives the y-intercept b = 3.
20
Hence the line equation is y = 2x + 3.
Solution:
m=
1
Midterm Exam 3
Spring 2013
Math 0120
Solutions
100 points total
1. [10 points] A company marginal cost function is M C (x) = 20x3/2 15x2/3 + 1, where x is
the number of units, and xed costs are $4000. Find the cost function.
Solution: C (x) =
M C (x) dx =
Midterm Exam 2
Spring 2013
Math 0120
100 points total
Solutions
1. (a) [10 points] Find f (2) if f (x) =
Solution:
e.
e is a constant. Hence, f (x) = 0 for any x and, in particular, f (2) = 0.
(b) [10 points] Find f (1) if f (x) = ex ln(x2 ).
Solution:
1
Midterm Exam 1
Spring 2013
Math 0120
100 points total
Solutions
1. [10 points] Find and simplify the dierence quotient
f (x + h) f (x)
for the function
h
f (x) = 3x + 2. It is assumed, that h = 0.
Solution:
f (x + h) f (x)
3(x + h) + 2 (3x + 2)
3x + 3h +
Final Examination
Math 0120 Final Examination
Sample
Name (Print)
ID #
Signature
.
.
Instructor (circle one):
Lecture time (circle one):
Instructions:
1. Show your University of Pittsburgh ID if requested.
2. Clearly print your name and PeopleSoft number
Absolute Value
Denitions
|x| =
x,
x0
x,
x<0
This notation means that |x| equals x when x 0 and |x| equals x when x < 0. For example,
|5| = 5, since 5 0; | 5| = (5) = 5, since 5 < 0, and etc.
This is a more general case.
x a,
|x a| =
(x a),
xa0
xa<0
=
x a,