Math 139
Quiz
Chapter 4
Name _
Fall 2013
Section _
NO CALCULATORS!
1.
Sketch the graph of the function, f ( x ) = log 2 ( x + 2) + 1 , labeling at least three
coordinate pairs. (2 points)
Also, where applicable, find the x- intercept, y-intercept, asympto
Object Oriented Programming
(FIT-II)
J. H. Wang
Feb. 24, 2014
Instructor & TA
Instructor
J. H. Wang ( ? )
Associate Professor, CSIE, NTUT
Office: R1534, Technology Building
E-mail: jhwang@csie.ntut.edu.tw
Tel: ext. 4238
Office Hour: 9:00-12:00 am, every
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Math 139 - Self Assessment
Calculus 2.7 - The Derivative as a Function
Review Problems
1. Sketching Functions Sketch the graph of each function. Clearly label intercepts (if any) and aysmptotes (if any):
(a) y = 3 sin(x )
(b) y = ln(x) + 3
(c) y = ex
(d)
Math 139 Exam #1
February 13, 2013
Problem(s) Score Total
Time: 1 hour and 25 minutes
Instructions: Show all work for full credit.
No outside materials or calculators allowed.
Extra Space: Use the backs of each sheet
for extra space. Clearly label when
Math 139 Exam #3
April 10, 2013
Problem(s)
Time: 1 hour and 25 minutes
Instructions: Show all work for full credit.
No outside materials or calculators allowed.
Extra Space: Use the backs of each sheet
for extra space. Clearly label when doing so.
Name
Math 139, Summer 2014
Name _
Sec. 6.2 - Sum and Difference Identities
1. Evaluate the following. Use the sum and difference identities if necessary.
a)
( )
( )
b)
(
)
c)
d)
2. Use the sum and difference identities to verify each identity.
a)
(
3. If cos
Project 3: Finding an Equation of a Line with Specied Slope
Which is Tangent to a Given Parabola
Algebraic Skills; - ,7 .
_o to use Special formulas to expand algebraic expressions'involving ra' dicalg .
- (a+b)2=:z_-2+2ab+l22 - "
(a+b)(a-b) =a2 62
cation
Math 139, Summer 14
Name _
Sec. 6.3: Double and Half Angle Identities
1. Given that sin
a) sin 2
1
with in Quadrant II, find:
2
c) tan 2
2. Given that cos
a)
d)
b) cos 2
d) angle
lies in what quadrant?
3
and is in quadrant III, find the values of:
5
b)
Math 139 Review from Previous Exams
10. Suppose that a given triangle has sides of length 5,
area of such a triangle in terms of t.
(where t is a constant). Find the
Pro'ect 1: A lication of s = 1'0 and v = rw to Two-Pulle S stems
Pulley systems provide an ideal environment for using the formulas s = r0 and
v =' m. Most of these problems can be solved more quickly by using ratios (which can be
justied by the: =11? a
Math 139, Summer 2014, Sec. 4.4 and 4.5
Exponential and Logarithmic Equations
Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the exponential equation. Express the solution set in terms of
Math 139, Sum 2014 HW Assignment
Basic Math and Algebra Review
Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the interval on a number line and write the inequality notation as well.
1) (
MW
Project 4: Of all the rectangles that could be inscribed in a given
ellipse, use optimization to nd the one with the largest area
Illustrative example 1:
2 2
(11) + (y :2) =1 sketch the
graph and then nd the rectangle with the largest possi
FINAL EXAM PRACTICE TEST
1. Evaluate the following
! 5 $
! $
a. cot # & + sec # &
" 3 %
" 6%
" 2%
" 1%
'
c. sin 1 $ ' + 2cos1 $
'
# 2&
# 2 &
MATH 139 Prof. B. Patiak
b. log 2 (87 )
d. 14cos 2 15 7
( )
2. Solve the following eq