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
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 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