MATH 3A - PRACTICE FIRST MIDTERM EXAM
Answers
Version A
1.
Version B
4
5
1.
1
8
a) 1, 2
2. a = 1, b = 4
b) 0, 0
2.
3. 1 cos() 1, use squeeze thm.
c) discontinuous at x = 0
3. lim f (x) = 0 = lim f (x)
Math 3A Exam 2 (Winter 2009)-Practice
Name: TAs Name:
Lecture Time: Discussion Time:
DIRECTIONS: Please do not open your exam until you are instructed to do so. Write your name and ll in the blanks co
MATH 3A Winter 2008
Midterm I Jan 28, 2008 Name: Perm #: Schedule of discussion class:
Instructions: The exam consists of 7 problems. You have 50 minutes to answer all questions. Please write full s
MATH 3A - PRACTICE FIRST MIDTERM EXAM
Spring 2009, Version B
Perm #:
Discussion time:
NAME:
No Calculators. Solve each problem in the blue book. Number your
solutions according to the corresponding pr
Math 3A
Winter 2016
Trigonometry Review
1.
What are the measures of the interior angles of an equilateral triangle?
Suppose the length of each the side of the equilateral
triangle is 2. Bisect the t
Definitions and Theorem Statements
The exam will include 10 definitions or theorem statements
2 of the following:
Tangent Line
limx!a f (x) = L
Vertical Asymptote
Squeeze Theorem
Continuity at a numbe
Calculus with applicatinna 1
Math 3A. Fall 2009
Instructur: Suukyung Jun Gambler 29111: M
Answer the flibwing E questinn. Shaw all your war]: far full credit- Garrett
answers with inmnsistent; war}:
Hang Pham
Assignment Homework 1 due 10/02/2015 at 11:59pm PDT
Math3A-100-F15-Chapman
1. (1 pt) A taxi company charges $1.70 for the first mile (or
part of a mile) and 10 cents for each succeeding tent
Denitions and Theorem Statements
The exam will include 10 denitions or theorem statements
2 of the following:
Tangent Line
limxa f (x) = L
Vertical Asymptote
Squeeze Theorem
Continuity at a number
Rem
Denitions and Theorem Statements
The exam will include 8 of the following:
Secant Line
Tangent Line
limxa f (x) = L
limxa+ f (x) = L
limxa f (x) = L
limxa f (x) =
limxa f (x) =
Vertical Asymptote
Sq
Denitions and Theorem Statements
The exam will include 5 of the following:
Derivative of a Constant
Power Rule
Constant Multiple Rule
Additivity Rule (A.K.A. Sum Rule)
The Number e (Any valid denition
Secant Line The line connecting two points on a curve
Tangent Line A line which intersects a curve at a point with the
same slope as the curve at that point
limxa f (x) = L For all > 0, there exists a
Derivative of a Constant (c) = 0
Power Rule
d n
dx x
= nxn1
Constant Multiple Rule (cf ) = cf
Additivity Rule (A.K.A. Sum Rule)
d
dx f
+g =f +g
The Number e The real number such that limh0
Alternative
Anti-derivatives:
An anti-derivative of a function f is a function F with F = f
Example: If f (x) = x2 then F (x) = x3 /3 is an anti-derivative of f
Because any two functions with the same derivative
Midterm 2 Practice Solutions
Tangent Lines
1
1. y = 2 x +
1
2
4
4. y = 5 x +
2. y = 4 2x
5. y = x
e
3. y = 2 x +
13
5
6. y = 1
e
2
Find the values of x where f (x) = 0.
1
4e1/3
1. x = 0, 3 , 5
4
4
3.
MATH 3A - PRACTICE SECOND MIDTERM EXAM
Answers
Version A
1.
2x 2x4
+5
y2
y
2.
a) 21 m/s
Version B
1. tan x tan y
2.
b) 2
b) 5 seconds
c) 4
3. 0.36
cos x
a)
| cos x|
3.
3x ln 3 3x+1
b)
4 1
x3
x
2
c)
MATH 3A - PRACTICE FIRST MIDTERM EXAM
Spring 2009, Version A
Perm #:
Discussion time:
NAME:
No Calculators. Solve each problem in the blue book. Number your
solutions according to the corresponding pr
MAT 3A Winter 2008
Midterm II February 18, 2008 Name: Perm #: Schedule of discussion class:
Instructions: The exam consists of 6 problems. You have 50 minutes to answer all questions. Please write f
Math 3A Winter 2009 Final Exam-Practice
Name: Perm #: TAs Name: Lecture Time: Discussion Time:
DIRECTIONS: Please do not open your exam until you are instructed to do so. Write your name and ll in the
Math 3A Exam 1 (Winter 2009)-Practice
Name: TAs Name:
Lecture Time: Discussion Time:
DIRECTIONS: Please do not open your exam until you are instructed to do so. Write your name and ll in the blanks co
MATH 3A, FALL 2011
MWF 1:001:50, CAMPBELL HALL
Instructor: Ken Goodearl, South Hall 6520
Oce hours: MWF 11:0011:50
Head Teaching Assistant: Elizabeth Leyton
Teaching Assistants: Maree Afaga, Kevin Bri
MATH 3A - PRACTICE SECOND MIDTERM EXAM
Spring 2009, Version B
Discussion time:
Perm #:
NAME:
No Calculators. Solve each problem in the blue book. Number your
solutions according to the corresponding p
MATH 3A - PRACTICE FINAL EXAM
Spring 2009, Version A
Perm #:
Discussion time:
NAME:
No Calculators. Solve each problem in the blue book. Number your
solutions according to the corresponding problems.
MATH 3A - PRACTICE FINAL EXAM
Spring 2009, Version B
Perm #:
Discussion time:
NAME:
No Calculators. Solve each problem in the blue book. Number your
solutions according to the corresponding problems.