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 sufficiently close to, but not necessarily equal to, a." or
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 the function f(x) graphed below, find the following.
Ans
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 _
a. Find lim ﬁx) dlYuL f. Find lim ﬁx) I
x—> — 8 x—
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 vary. Values of f(x) must approach the same number for xs
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 rules that simplify the process!
The Constant and Power
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) to ﬁnd the following values, if they exist or are deﬁned
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) lim x ‘1 =Lu{m (_x D“ H)
 x—>1 x3—1 xs] (1—1)(x‘+1x+
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.
5. (l?
se limit properties to evaluate the followin
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 caieuiator.
1. For the function f (x) graphed below, ﬁnd
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 asymptotes uslng infinite limits.
12. (8 points) For eac
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 approximation to obtain a possible value for the following
Unit
2
Name _
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 Chain Rules to find
derivatives of arithmetic combinat
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 Simplify.
.a) ﬁx) = (x3 — 4x + 5)(2x2 + 3)
i—"(ﬁ = (13—H7c+53
Monroe Community College
DEPARTMENT OF MATHEMATICS
MTH 210: Calculus I
Course Information Sheet Fall 2015
Instructor:
Mary Cameron
Office:
8 550
Email: mcameron@monroecc.edu (preferred)
Phone Extension: 2963
Office Hours:
Monday 9 10 and 1 2 in 8550
Mon
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 llmlts at r: and limits at plus and mmus inﬁnity
003.7
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 Rule
an
a
n
b
b
Negative Exponent Rule
a n
n m
a1 = a
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(x) = 5 sin x — 3ex
g'm = 5cosx  3e."
19) (2 POintS) f
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 =
2
2
2
1
tan
Quotient Identities:
sin
tan
cos
Even
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
23. (4 points). U'se‘the graph ofﬂx) to identify'th‘
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
x=
III

ax2+bx = 0
Factor out GCF

Ex: px(x + q) = 0
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 numerically, graphically, and algebraically '
27. (12 points)
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 and limits at plus and minus Infinity
003.7 Describe hon
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
3  ’
xu +1.02% +5.63," +20¥gj + I513” +6135 rjb
b)
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 speciﬁed point P. Write the equation for the
tangent line
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 DIFFERENTIATION
11 15
E. ANTIDERIVATIVES AND INTEGRATION
16