C O N TA C T U S ( / c o n t a c t )
D I R E C T O RY ( / p e o p l e / d i r e c t o r y / a l l )
Chapter 3 Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions
Derivative of a Constant Function
( c )=0
( x ) =1
The Power Rule If n is a positive integer, then
( x )=n x n1
The Constant Multiple
Chapter 4- Applications of Differentiation
4.1 Maximum and Minimum Values
Absolute maximum and minimum definition
Let c be a number in the domain
D of a function f . Then f (c) is the
Absolute maximum value of f
D if f ( c ) f (x ) for all
Chapter 5 Integrals
5.1 Areas and Distances
the area A
of the region S that lies under the graph of the continuous function f is
the limit of the sum of the areas of approximately rectangles
A= lim R n [ f ( x1 ) x + f ( x 2 ) x + f (x n) x ]
Chapter 2 Limits and Derivatives
2.1 The Tangent and Velocity Problems
The word tangent is derived from the Latin word tangens, which means touching. Thus, a
tangent to a curve is a line that touches the curve. In other words, a tangent line should have
MIS 0855 Data Science (Section 005) Fall 2016
Thursday 5:30 8:00 PM, Alter Hall 232
Updated on Oct 25 with a new schedule
Dr. Min-Seok Pang (Ph.D., University of Michigan)
Speakman Hall 201E, [email protected]
Office Hours: Monday, Thursday 3
1. Sketch the angles
on separate graphs. Are they coterminal angles?
2. Use the triangle below to find the following trigonometric functions
3. Solve the following right triangle.
Find the exact values for the following trigonometric functions.
1. sin 4
2. sec 5
3. cos 5
4. tan 7
5. csc 5
7. Suppose that tan = 4 and sin > 0. Find the remaining 5 trigonometric functions.
8. Find t
1. Express the following equations in exponential form
(a) log5 ( 15 ) = 1
(b) ln(t + 1) = 5
2. Express the following equations in logarithmic form
(a) 82 =
(b) ex = 2
3. Evaluate the following expressions
1. Let f (x) =
(a) Find the domain of f
(b) solve the inequality f (x) 0
2. Let f (x) =
Find f (a), f (a + h), and the difference quotient
f (a+h)f (a)
where h 6= 0.
3. Consider the following fun
1. The graph of y = f (x) is given below along with four transformations. Match each equation
with its graph. Write the number of the graph next to the proper equation.
(a) y = 13 f (x)
(b) y = f (x + 4)
(c) y = f (x 4) + 3
1. Suppose that f (x) =
25 x2 and g(x) =
(a) Find the domain of both f and g
(b) Find (f g)(x) and state its domain.
(c) Find ( fg )(x) and state its domain.
2. Use the table below to evaluate the given expressions.
1. Useqthe Laws of Logarithms to expand the expression
log (x2 +1)(x
2. Solve the following equations for x.
(a) e2x + 4ex 21 = 0
(b) log9 (x 5) + log9 (x + 3) = 1
3. How long will it take for an investment of $
MATH 1015 TEST 1 REVIEW . Chapters 1,2,3, and Base 2
1. The loose toothpicks pictured are not organized in a way that fits with the structure of the
decimal system. Show how to arrange the appearance ofthese bagged and loose toothpicks so
that the same nu
Math 1015 . V - REVIEW TEST 3 Chapters 6 8L 7
1. For each of the following story problems, write a division problem that
solves the problem, give an appropriate answer to the problem, and say
which of the two interpretations of division is used (the "how
Math 1015 Review forTest2 Chapters 4 and 5
l. (4.1) A 40member club will elect a president and
then elect a Vice president. How many possible
outcomes are there? (hint: Allen as president
with Bob as vice president is a different outcome
as Bob as preside
APPLICATION FOR EMPLOYMENT
Present address (street, city, state, zip):
Permanent address (street, city, state, zip):
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RECOMMENDED HOMEWORK PROBLEMS
Text: 1. James Stewart, Calculus, Early Transcendentals,
2. Math 1042 ADDITIONAL Homework Problems
8th Edition, Cengage Learning.
You are expected to solve ALL of the problems listed here and write out
Calculus Midterm 1 Problem Solution Videos
Q17 , Section 2.2, James Stewart Calculus 8th Edition
Q33 , Section 2.2, James Stewart Calculus 8th Edition
Q35 , Section 2.2, James Stewart Calculus 8th Edition
Stewart Calculus: ET - Sectio
Answer-Keys of Review Problems for Test 1
lim f (x) =d.n.e.
(f) f (4) is undefined.
lim f (x) = 3 = lim f (x) = 1,
x = 0 and x = .