Calculus II - Core Concept Cheat Sheet
01: Introduction to Calculus II
Study Tip
Know Prerequisite Knowledge
What is Calculus II
Calculus is the study of how things change. In a first
Calculus course, you learn topics such as Limits,
Differentiation, and
Calculus III - Core Concept Cheat Sheet
17: Iterated and Double Integrals
Integrating a Two Variable Function
Order of Integration
Integrating a two variable function with respect to x yields a
one variable function of y. Similarly, integrating a two
vari
Calculus Core Concept Cheat Sheet
06: Limits
Key Terms
Limits at Vertical Asymptotes
The Limit of f(x) as x Approaches a: The value to which
the output (dependent variable) of f(x) approaches as x
(independent variable) approaches the number a.
Velocity
Calculus Core Concept Cheat Sheet
16: Riemann Sums and the Definite Integral
Key Terms
Properties of the Definite Integral
Area Problem: Problem consisting in finding the area of a
region of the xy-plane.
Partition of [a, b]: Finite and strictly increasin
MATH 150/6RACEY
EXAM I/CHAPTER 1
100 POINTS POSSIBLE
YOUR WORK MUST SUPPORT YOUR ANSWER FOR FULL CREDIT TO BE AWARDED!
NO CALCULATORS!
1. (8 POINTS, 2 POINTS EACH) Use fhe graph of y =f(x) shown beiow To find
each limit, if if eXis’rs. If The li-mi‘i' d
MATH 150/GRACEY
NAME_
EXAM 2/CHAPTER 2
100 POINTS POSSIBLE/BOX YOUR FINAL ANSWER
SHOW ALL WORK FOR FULL CREDIT!
1.
(5 POINTS)
(48 POINTS) Problems 2-7. Find the derivative of the functions below with respect to
the independent variable. Each item is worth
MATH 150/GRACEV NAN!wa
EXAM Z/CHAPTER 2
100 POINTS POSSIBLE/BOX YOUR FINAL ANSWER
SHOW ALL WORK FOR FULL CREDIT!
1. (5 POINTS)
The equatien gives the position 5 2 ﬁt} of a body moving on a coordinate iine {s in meters; is in seconds},
{5 ,
s {In}
‘When
NAME
HOMEWORK % EXAM % QUIZ %
Completely analyze the following function. Be sure to write “none” if this function does not have a characteristic listed
below. I
2
3C
Consider the function f(x) =—;————.
x‘ —16
1. Give the ordered pairs representing the i
9?: E;
MATH ISO/GRACEY NAME ﬁg?!
EXAM 4/37, 3.9, 4.1—4.5 HW % EXAM+°A QUIZW‘YD
100 POINTS POSSIBLE/BOX YOUR FINAL ANSWER
SHOW ALL WORK FOR FULL CREDIT!
(56 POINTS) Problems 1-8. Evaiua’re The deﬁnife im‘egmls and find fhe indefinite
imegmfs: Each quesT