7.2: PARTIAL DERIVATIVES
(Mathematica was used to produce these computer graphics.)
Note: The coordinate axes are oriented in an unusual way:
The large black dot indicates the point (1, 2, 3).
Figure #1: Graph of f ( x, y) = -5 x 2 + y3
Figure #2: The tan
Math 121
Name: _
QUIZ #4 (SAMPLE QUESTIONS)
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers; write units where appropriate!
No notes or books allowed.
USE A SCIENTIFIC CALCULATOR!
1) Find th
QUIZ #3 (SAMPLE SOLUTIONS)
USE A SCIENTIFIC CALCULATOR!
1) For parts a) and b), sketch the graph of f. You must:
Find and label all critical points and inflection points (if any).
Classify all critical points as relative maximum points, relative minimum
Math 121
Name: _
QUIZ #3 (SAMPLE QUESTIONS)
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers; write units where appropriate!
No notes or books allowed.
USE A SCIENTIFIC CALCULATOR!
1) For par
QUIZ #2 (SAMPLE QUESTIONS)
PART 1 (NO CALCULATORS!)
1) Let f ( x) =
f ( x) =
=
4x
. Find f ( x) . Simplify your answer. (6 points)
x +1
2
Lo D (Hi) - Hi D (Lo)
the square of what below
s
(x
=
+ 1) Dx ( 4 x ) - ( 4 x ) Dx ( x 2 + 1)
(x
(x
=
=
2
2
(Quotient
Math 121
Name: _
QUIZ #2 (SAMPLE QUESTIONS)
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers; write units where appropriate!
No notes or books allowed.
PART 1 (NO CALCULATORS!)
1) Let f ( x)
QUIZ #1 (SAMPLE QUESTIONS)
PART 1 (NO CALCULATORS!)
1) Find the following limits without making a table. Write or - when
appropriate. If a limit does not exist, and and - are inappropriate, write
DNE. Box in your final answers. (13 points total)
a) lim
x
Math 121
Name: _
QUIZ #1 (SAMPLE QUESTIONS)
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers; write units where appropriate!
No notes or books allowed.
PART 1 (NO CALCULATORS!)
1) Find the fo
FINAL (SAMPLE SOLUTIONS)
USE A SCIENTIFIC CALCULATOR!
1) Approximate the area under the graph of f ( x) = ln x from a = 4 to b = 10 by
finding a Left Riemann Sum using 3 rectangles of the same width. Round off to
four decimal places whenever you need to r
Math 121
Name: _
FINAL (SAMPLE QUESTIONS)
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers; write units where appropriate!
No notes or books allowed.
USE A SCIENTIFIC CALCULATOR!
1) Approxima
Math 121
Name: _
QUIZ #4 (SECTIONS 4.3, 4.4, 5.1, 5.2)
MATH 121 FALL 2003 KUNIYUKI
105 POINTS TOTAL, BUT 100 POINTS = 100%
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers; write units where
QUIZ #3 (SECTIONS 3.1, 3.2, 3.3, 3.6)
SOLUTIONS
MATH 121 FALL 2003 KUNIYUKI
105 POINTS TOTAL, BUT 100 POINTS = 100%
1) Sketch the graph of f ( x) = x 4 - 4 x 3 + 3. You must:
Find and label all points at critical numbers and inflection points (if any).
Math 121
Name: _
QUIZ #3 (SECTIONS 3.1, 3.2, 3.3, 3.6)
MATH 121 FALL 2003 KUNIYUKI
105 POINTS TOTAL, BUT 100 POINTS = 100%
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers; write units where
QUIZ #2 (SECTIONS 2.4, 2.5, 2.6, 2.7)
SOLUTIONS
MATH 121 FALL 2003 KUNIYUKI
105 POINTS TOTAL, BUT 100 POINTS = 100%
PART 1 (USE A SCIENTIFIC CALCULATOR!): 31 points
1) The position function of a particle in inches is given by s ( t ) = 5 t 3 + 4 t , where
Math 121
Name: _
QUIZ #2 (SECTIONS 2.4, 2.5, 2.6, 2.7)
MATH 121 FALL 2003 KUNIYUKI
105 POINTS TOTAL, BUT 100 POINTS = 100%
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers; write units where
QUIZ #1 (SECTIONS 2.1, 2.2, 2.3)
SOLUTIONS
MATH 121 FALL 2003 KUNIYUKI
105 POINTS TOTAL, BUT 100 POINTS = 100%
PART 1 (NO CALCULATORS!): 82 points
1) These instructions apply to questions a) through i):
Find the following limits without making a table. Wr
Math 121
Name: _
QUIZ #1 (SECTIONS 2.1, 2.2, 2.3)
MATH 121 FALL 2003 KUNIYUKI
105 POINTS TOTAL, BUT 100 POINTS = 100%
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers; write units where appro
MATH 121: HOMEWORK #5
SECTIONS 5.3, 5.4, 5.6, 7.1, 7.2, 7.3
FALL 2003
Write your name and clearly separate sections on your homework!
You may want to photocopy this, especially if you plan to take Math 122!
(Chapter 7 is also covered in Math 122.)
Show wo
MATH 121: HOMEWORK #4
SECTIONS (4.1), (4.2), 4.3, 4.4, 5.1, 5.2
FALL 2003
Write your name and clearly separate sections on your homework!
Show work where appropriate, and use good form and procedure, as in class!
This is due when you take Quiz 4.
Graded o
MATH 121: HOMEWORK #3
SECTIONS 3.1, 3.2, 3.3, 3.6
FALL 2003
Write your name and clearly separate sections on your homework!
Show work where appropriate, and use good form and procedure, as in class!
This is due when you take Quiz 3.
Graded out of 10 point
MATH 121: HOMEWORK #2
SECTIONS 2.4, 2.5, 2.6, 2.7
FALL 2003
Write your name and clearly separate sections on your homework!
Show work where appropriate, and use good form and procedure, as in class!
This is due when you take Quiz 2.
Graded out of 10 point
MATH 121: HOMEWORK #1
SECTIONS 2.1, 2.2, 2.3
FALL 2003
Write your name and clearly separate sections on your homework!
Show work where appropriate, and use good form and procedure, as in class!
This is due when you take Quiz 1.
Graded out of 10 points.
*
SOLUTIONS TO THE FINAL
MATH 121 FALL 2003 KUNIYUKI
126 POINTS TOTAL, BUT 120 POINTS = 100%
1
from a = 2 to b = 14 by
x
finding a Left Riemann Sum using 4 rectangles of the same width. Round off to
four decimal places whenever you need to round off. (14 po
Math 121
Name: _
FINAL
MATH 121 FALL 2003 KUNIYUKI
126 POINTS TOTAL, BUT 120 POINTS = 100%
Show all work, simplify as appropriate, and use good form and procedure (as in class).
Box in your final answers; write units where appropriate!
An appropriate shee