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 corresponding to your lecture time, TAs name, and discuss
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)
x0
4.
x0+
1
2
b)
a)
5. f (0) = 2 and f (3) = 7, use I
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 solutions, not just answers. Answers without justif
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) (3x + 2) ln x + x2 + 2
4.
4.
5. 1.25 m3
a) -1
3
m/min
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 problems. No points will be
given for answers with no exp
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}: may not be given credit.
Perm nu mh-er: M
H II
.5
TA
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 tenth of a mile
(or part). Express the cost C (in dollars)
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
Removable Discontinuity
Jump Discontinuity
Intermediate Va
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
Squeeze Theorem
Continuity at a number
Continuity from th
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 will suce)
Derivative of ex
Derivative of ax
Product R
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 such that
0 < |x a| < implies |f (x) L| <
limxa+ f (x)
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
Alternatively limn (1 +
d x
x
dx e = e
d
ax dx ax = ln(a)ax
Deriva
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 must dier by
a constant, if F is one anti-derivative of
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. x =
2. x = 0, 1
4. x = 0, 1, 3
Additional Dierentiatio
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 problems. No points will be
given for answers with no exp
MATH 3A - PRACTICE FINAL EXAM
Answers
Version A
1.
2.
ey + 3y cos x
3 sin x xey
a) D = cfw_x = 0, x = 1
y = 0 hor. asympt,
x = 1 vert. asympt.
Version B
1.
2.
3. 2:12 pm
4.
a) D = (, 1) (0, )
1
y = 2 hor. asympt,
no vert. asympt.
b) x > 0 increasing,
x <
MATH 3A - PRACTICE SECOND 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 problems. No points will be
given for answers with no ex
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 full solutions, not just answers. Answers without j
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 blanks corresponding to your perm number, lecture time
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 corresponding to your lecture time, TAs name, and discuss
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 Brighton, Teddy Einstein, John Mangual
[all have oces in S
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 problems. No points will be
given for answers with no ex
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. No points will be
given for answers with no explanation
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. No points will be
given for answers with no explanation
Midterm 2 Practice
Dierentiation Rules
For each of the following, nd f (x).
1. f (x) = e2 + 3 x + 4x
10. f (x) =
2. f (x) = cos(tan x)
11. f (x) = ex sin(x) ln(x)
3. f (x) = x +
1
x2
7
12. f (x) = e
ln(x2 + 1)
4. f (x) = tan
5. f (x) =
x+
6. f (x) =
3x4
2