Quiz One, MTH 121, Fall 2000
1. Find the domain of the following function:
a) cfw_ x |
x 1
b) cfw_ x |
x > 1
f ( x) =
1
x2 1
c) cfw_ x | 1 < x < 1
d) cfw_ x |
x < 1 or x > 1
Answer: d (5 points)
Solution: we need x 2 1
0 because x 2 1 is under a radic
M 121 Quiz 5.
No Calculator.
Show Work!
1.
Use the definition of derivative to prove that if
formula will get you zero credit.
f ( x) = 3 x 2
f ( x) = 6 x Note: quoting the
lim 0
h
3( x + h) 2 3 x 2
3 x 2 + 6 xh + h 2 3 x 2
6 xh + h 2
= h lim 0
= h lim 0
Quiz 4, Math 121.
No Calculators Allowed!
You may use your brain all that you like.
1.
f ( x) = x 2 + 3 x + 1, f ( x) =
( x + h) 2 + 3( x + h) + 1 ( x 2 + 3x + 1)
x 2 + 2 xh + h 2 + 3x + 3h + 1 x 2 3 x 1
= h lim 0
h lim 0
h
h
2
h + 2 xh + 3h
= x lim 0
= h
Math 121, Quiz Three.
All questions are short answer.
For questions 1- 3: Suppose that
f ( x) =
x
for x 0 , and undefined for x = 0 . You might find a
|x|
graph to be helpful.
1.
2.
3.
x
lim
f ( x ) = 1 because when x > 0,
x
x
= =1
|x| x
lim
f ( x) = -1 b
Math 121, Quiz Two. 4 points each; score is out of 25.
1. What best describes the path of a particle whose position is descried by the following parametric
equations: x(t ) = cos(2t ), y = sin( 2t ),0 t 2
(1,0).
b) Travels in a counterclockwise direction
M 121 Quiz, 13 October 2000.
Show Work. Answers without work will be counted as being wrong.
1-2 Suppose we are given:
f (0) = 1, f (0) = 2, f (1) = 0, f (1) = 1, f (2) = 1, f (2) = 1
g (0) = 2, g (0) = 1, g (1) = 1, g (1) = 0, g (2) = 2, g (2) = 1
( f g
M121 Quiz. Show work.
1. If
y = ( x 2 + 1) sin( x ) ,
dy
=
dx
Note: just copying what your calculator says will result in no credit. Show work!
ln( y ) = ln( x 2 + 1) sin( x ) ) = sin( x) ln( x 2 + 1)
d
d
ln( y ) =
(sin( x ) ln( x 2 + 1)
dx
dx
1
y
1
y
dy
Show your work; answers without work are WRONG.
1. We are enclosing a field by a rectangular fence. One of the sides is bordered by a straight river, hence
we need to have only 3 sides of fencing. The side parallel to the river costs 100$ per linear foot,
M121 Fall 2000, Exam Three. Show all Work!
1. (20) Boyles law states that when a sample of gas is compressed at a constant temperature, the pressure
and volume satisfy PV = C where C is a constant, P is pressure and V is volume. Suppose that at a
certain
M121 Exam 2.
Show your work. You will be graded out of 100 points; there are 30 possible points in part I and 90
possible in part II.
Part I. 5 each
1.
f ( x) = cot( x); f ( x ) = b; use the quotient rule:
cos( x ) (sin( x)(cos( x ) (sin( x ) cos( x) (si
M121 Quiz 8
Fall, 2000
1. State the Mean Value Theorem.
If is continuous on [a, b] and differentiable on (a, b) there exists a number c, a < c < b such that
f (c) =
f (b ) f ( a )
(b a )
f ( x ) = 12 x( x 1) 2 ( x + 2)( x 4) find (Please Note: the derivat
Math 121, Exam One.
Show work on the short answer sections.
Note: some questions are short answer; others are multiple choice.
Multiple Choice Part. 5 points each.
1-4. A runner wants to find the optimum training level to run a 10K race. He looks at his t
Math 115
Exam Three.
Show work where appropriate.
Multiple Choice (5 points each):
1. If y
a)
ln x , y
1
2 ln x
1
x
b)
Solution: y
1
2
c)
1
2
ln x
ln x
1
2x ln x
1
2
1
2
ln x
Answer: C
Typical mistake: forgetting the ln x
2. If y e x , y
2
2
b) x 2 e
Math 115, Fall 2002
Quiz One.
1. If g x
x 0 and x
the domain for g is: (c) All real numbers except for x 0 or x 2 (i. e.,
3
xx 2
2)
2-3. If f x x 2 and g x
2. f g x
1
x1
3. g f x
1
x2 1
x
,
1
x
(a)
4. Short answer:
1
x1
(c)
2
1
x
In other words, factor
M115 Exam Four, Fall 2002. Show work where appropriate.
Multiple Choice (5 Each)
1. e 2x dx 1 e 2x C D
2
a) e 2x C
b) 2e 2x C
2. x 2 1dx | 2 1 x 3 x
03
2
0
14
3
a)
C
3.
2
x
a) 4 x
b)
11
3
8
3
14
c) 3
C
3 x dx 2x
3
2x 2 C
1
2
1
e 2x1 C
00
2
14
3
1
2
d)
M115 Exam Two
Show all work.
Short Answer. These are worth 20 points each.
1 Dont Simplify these.
a) (10 points) If y 3x 2
2 x
3
x
5
14x 2
1, find y 6x
b) (10 points) if y 3x 3 2x 5 , find y 5 3x 2 2x
2. Suppose that g x x 4
4
x
1
2
3x
2
3
35x 2
9x 2 2
M115 Exam 2
Show all work.
Short Answer. These are worth 20 points each.
1. Dont simplify these.
a) (10 points) If y 2x 3 3 x
2
x
7
12x 2
2, find y 6x 2
b) (5 points) if y 4x 4 3x 6 , find y 6 4x 4 3x
2. Suppose that g x x 4
5
3
2
1
2
x
2x
2
5
42x 2
1
M115 Quiz Two.
1. The slope of the line 2x 3y 6 is:
a) 2
b) 3
Answer: 2x 3y 6
c) 2
3
3y 6
d)
2x
3
2
e)
y2
2
3
2
3
f)
3
2
x
e
2. You have a line with slope 3 which contains the point 1, 2 . Which of the following points
is also on this line? (Only one of t
Math 115 Exam One
On the short answer section, show work.
Multiple choice problems are worth 6 points each, and short answer problems are worth 10
points each.
1. Consider the graph of f x x 2 1. Feel free to use your calculator to observe the
graph. Whic
M115 Quiz 8.
Show work.
1. x 2 e 2x dx
x3
1
2
e 2x C
x dx ln |x|
2
3
x2 C
2.
1
x
3.
12x 2
x
x
2x dx
1
x
1
3
dx
2
3
(hint: do some algebra first)
1
x
2xdx ln |x| x 2 C
4. If g x 2x e x and g 0 1 then find g x .
g x dx 2x e x dx x 2 e x C g x
g 0
M115 Quiz 7
1. Solve for x: 350e 2x 700
a) x
1
2
e 2x 2
2. y
a) y
y
b) x e 2
ln 700
ln e 2x ln 2
x
.
ln x
ln x 1
ln x 2
1 ln x x 1
x
2
ln x
3. y
ln x
b) y x
ln x 1
ln x 2
1
2
1
2
1
2
ln 2
ln 2 : D
c) y x ln x
d) y
1
1
ln x
x
ln x
2
:A
1
2 ln x
y
x
d)
M115 Quiz 6, v2. 1-3 are worth 30 points each; 4 is worth 10 points.
1. Find
dy dx
dy : dx 2xy 3 8y 3x 2 y 2
x2y3
2y 2 8 3x 2 y
4y 2 1 Solution: 2xy 3 3x 2 y 2
dy dx
8y dy 0 dx
2xy 3 8y
3x 2 y 2
dy dx
2. Suppose that the price p in dollars and the demand
M 115 Quiz Three 10 points each (70 maximum)
1-3 Find the limit, if it exists.
1 . lim x
x2 9 3 x 3
Solution: lim x
x2 9 3 x 3
lim x
3
x 3 x3 x 3
lim x
3
x3 1
6
"b"
a) 3
b) 6
c) 0
d) does not exist
2. lim x a)
1 3
x 2 2x1 3x 3 7
Solution: lim x c) 0
x 2
M115 Quiz 6, v1. 1-3 are worth 30 points each; 4 is worth 10 points.
1. Find
dy dx
dy : dx 8x 3x 2 y 2 2x 3 y
x3y2
8 3xy 2 2x 2 y
4x 2 1 Solution: 3x 2 y 2 x 3 2y dy dx
8x 0
2x 3 y dy 8x dx
3x 2 y 2
2. Suppose that the price p in dollars and the demand x
Solution to Problem 69
Congratulations to this week's winner
Nathan Pauli
Partial solutions were also received from Joshua Durham, Ray Kremer. Additional partial solutions were submitted by Jure Velkavrh and Ivan Lisac, Maxim Ovsjanikov, Philippe Fondanai
Solution to Problem 68
Congratulations to this week's winners
Kenny Albright, Mike Behrens, Nathan Pauli, Ray Kremer
Correct solutions were also sent in by Bradley student Benjamin Brown and Bradley faculty member Ollie Nanyes. Correct solutions were also
Solution to Problem 67
Congratulations to this week's winner
Scott Peters
Correct solutions were sent in from Bradley students Kenny Koch, Michelle McCluer, Nathan Pauli, Ray Kremer, Kyle Ambroso, Paul Leisher; a partial solution was submitted by Courtney
Solution to Problem 66
Congratulations to this week's winner
Bradley McManus
All Correct solvers had the same solution. Bradley was chosen as the winner by a random drawing. Correct solutions were also received from Bradley students Tim Callahan, Julie Fa
Solution to Problem 65
No complete solutions were received, but partial solutions were sent in by
Nathan Pauli, Ray Kremer, Mike Mitchell
Correct solutions were received from Ivan Lisac, Burkart Venzke, Philippe Fondanaiche. A number of incorrect solution
Solution to Problem 64
Congratulations to this week's winners
Nathan Pauli, Anna McCullough, Tracy Thatcher
Further correct solutions were also received from Silvain Vinassac, Al Zimmermann, Burkart Venzke, Philippe Fondanaiche, William Webb.
The easiest