Notes Packet
Chapter 2: Limits
UNIT
2.2 Definitions of Limits
CO3.1 Write an intuitive, English definition of limit., e.g., Def: lim f x L "f(x) can be made arbitrarily
x a
close to L by making x suff
Name _
Unit
CO3.3a Approximate limits, including left and right hand limits at c [2.2, 2.4] and limits at
plus and minus infinity [2.5], numerically and graphically [2.2], using a calculator.
1.
For t
WWW MTH 210 Exam #1
. h t 1 &2 F 112015
1. (15 pomts) For the function f (x) graphed below, ﬁnd the following. ap ers 7 ( a )
Answer with a number, 00 ,  —OO, undeﬁned, or dne (does not exist).
, I
MTH 210 COURSE REVIEW SOLUTIONS
Part I: Limits and Continuity
1. a. The values of f (x) can be made arbitrarily close to 9 for all x in some
sufficiently small interval containing 4.
b. Answers may va
Chapter 3: Derivatives
Notes Packet
UNIT
3.3 Rules of Differentiation
The derivative of f can always be evaluated using the limit definition for the
derivative. This chapter presents differentiation r
Name
3.
Consider x = :
x—>1_
x—>1“"
lim
x—)l f
Consider x = 3:
x—>3_
1:63+
£131" (36)
f
4.
Practice Quiz A2
MTH 210 — Spring 2015
Tutoring Assistance Permitted
(lﬂ points) Use the graph of f (x) t
Name
2.3 Techniques for Comguting Limits
603.4 Using rulesr evaluate limits algebraically, including left and right hand limits at c.
9. (8 points) Find the following limits:
4 2._ 1.
a) l
Name
Practice Quiz A3
MTH 210 — Spring 2015
Tutoring Assistance Permitted
2.3 Technigues for Computing Limits
003.4 §lng rules, evaluate limits algebraically, including lett and right hand limits at c
N goluﬁcmso
. Name
{35.33.3533 stigmiexérnate iémits. massing heft and right hand timits at e {2.2, 21%} and iim‘tts at nice and
minus in’ihﬁéy :25; semesieaiiy and giehhicaliy {2.2%. using a ca
Name I Practice Quiz A5
MTH 210 — Spring 2015
2.4 infinite Limits Tutoring Assrstance Permitted
003.5 Describe a function that is unbounded at cin terms of infinite limits.
003.6 Describe vertical asy
Name
2.2 Definitions of Limits ;
003.3 Approximate llmlts, including left and rlght hand limits at cand llmits at plus and minus Infinity, numerically
and graphically
l. (3 points) Use numerical app
Unit
2
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CO4.6 Know derivatives of powers of x, all six trigonometric, exponential and logarithmic functions. [3.3, 3.5,
3.9]
CO4.7 Apply Sum, Difference, Constant Multiple, Product, Quotient and
Name
Practice Quiz BZ
3.4 The product and Quotient Ruies MTH 210 ‘ 1351113015
Tutoring Assistance Permitted
7. (8 points) Use the product rule to ﬁnd the derivative of the following functions Simplif
Monroe Community College
DEPARTMENT OF MATHEMATICS
MTH 210: Calculus I
Course Information Sheet Fall 2015
Instructor:
Mary Cameron
Office:
8 550
Email: [email protected] (preferred)
Phone Extensi
Nameﬂ  Practice Quiz A7
2.5 Limits at Infinity: lcontinuedi MTH 210  Spring 2015
. . . _ Tutoring Assistance Permitted
003.4 Using rules, evaluate llmlts algebraically, Including left and nght hand
Properties of Exponents
a > 0, b > 0, a 1,b 1, n, m are real numbers
Rules of 1
a0 = 1
Product Rule
an am = an+m
Quotient Rule
an
a n m
am
Power Rule
a
Product Power Rule
ab n a nb n
Quotient Power
Name
Practice Quiz B3
3.5 Derivatives of Trigonometric Functions MTH 210 ‘ Spring 2015
Tutoring Assistance Permitted
11. Find the derivatives of the following ﬁmction's. Simplify.
a) (2 points) g(
Reciprocal Identities:
1
1
sin =
csc =
csc
sin
cos =
1
sec
sec =
1
cos
tan =
1
cot
cot =
Power Reducing Formulas / Half Angle Formulas
1 cos 2
1 cos
sin
sin2 =
2
2
2
1 cos 2
1 cos
cos
cos2
Name
Practice Quiz A8
2.6 Continuity i MTH 210 — Spring 2015
003.2 Recognlze that a functlon ls continuous at afar fimctlons given 'Iiuineritmllyr graphically, and algebraically Tummg “15‘3"” Pmnw
I Summary of Seven
Equation Solving
Techniques
 #s
Only
II
=
x2 or
and xs
(x
)
2
Rewrite:

Rewrite (Distribute,
Combine like terms):
ax = k
=0

ax2+bx+c = 0

Divide both sides by
coefficient of x
Name ' _  Practice Quiz A9
MTH 210 — Spring 2015
. . . Tu ' As ‘ t P ‘tted
2.6 Continuity geontmued! . [01mg 5‘5 me em”
603.2 Recognize that a function is continuous at cfor functions given numerical
Name 7 Practice .Quiz A6
2.5 Limits at Infinity MTH 210  Spﬂﬂg 2015
_ _ _ _ Tutoring Asaistance Permitted
003.4 Using rules, evaluate limits algebraically, including left and light hand limits at c a
Name
Practice Quiz Bl
3.3 Rules of Differentiation MTH 219 ' Fa“ 20,15
. . . Tutoring Asmstance Permitted
l. (4 p01nts) Practice usmg useﬁil formulas!
a) Use the Binomial Theorem to expand: (x + y)6
Name
3.1 Introducing the Derivative
31.
a) [#10]
b) [#22]
Practice Quiz All
MTH 210 — Spring 2015
Tutoring Assistance Permitted
(12 points) Find the slope of the line tangent to the ﬁmction at the spe
MTH 210
CALCULUS I
COURSE REVIEW QUESTIONS
(REVISED SPRING 2012)
TABLE OF CONTENTS
TOPIC
PAGE NUMBER(S)
A. LIMITS AND CONTINUITY
15
B. DIFFERENTIATION
56
C. GRAPH ANALYSIS
6 10
D. APPLICATIONS OF DIFF