Chapter 8 Sequences and Series of
Functions
Section 8.1
1.
(a)
(d)
(f)
(g)
(h)
(k)
(n)
(b)
(e)
(d)
f(x) = 0. To prove this, fix x, call it x0 E [0,1], and show that lim 1, (x0) = 0. Let s > 0 be given.
nsoo
We need to nd n* E N such that |f(x0)fn(xo)| < 5
Chapter 9 Vector Calculus
Section 9.1
2. Ifthe points are A(3,3,3), B(2,1,1), C(5,4, 2), then d(AB)=1/E,'d(B,C)= 3%, d(A,C)=1/g. Since,
[auto]2 +[d(A,B)]2 =[d(B, 6)]r2 , this is a right triangle.
4. Let (x, y,z) be a point equidistant from the given point
Chapter 2 Sequences
Section 2.1
1 _ . . .
1. < 0.02 <21 < (0.02)1In +1 <2 n > 2499. Thus, 1f 11* = 2,500 , then for any n 2 11* the given inequahty
Vn+1
will be true.
2. (a) We prove that lim an = 0. Let s > 0 be given. We need to nd 11* EN 50 that Ian
Chapter 10 Functions of Two Variables
Section 10.2
1. (a) Domain is the set of all points (Ly) such that :c2 + (y +1)2 5 1.
(c) Domain is the set of all points (x, y) in mg.
2. (a) We will prove that the value of the limit is 0. Let s > 0 be given and cho
Chapter 4 Continuity
Section 4.1
2. (a) No, f is not continuous at x = 0 , thus not continuous at every point in the interval.
(b) Yes, f is right continuous at every point in the interval.
(c) Yes, f is continuous at every point in the interval.
3. (
Chapter 3 Limits of Functions
Section 3.1
1. lim f (x ) = 00 if and only if for any real K > 0 there exists a real number M > 0 such that f (x) < K
xroo
provided x 2 M and x is in the domain of f.
2. (a) We will prove that lim f (x)= 2. Therefore, let a >
Quiz # 6093 BL:3.8 PTS: 0.5
Strega Nona
By: Tomie DePaola
In a town in Calabria, a long time ago, there lived an old lady everyone called Strega Nora, which
meant Grandma Witch. Although all the people in town talked about her in whispers, they all went
t
Quiz # 30305 BL:3.3 PTS:0.5
Dear Children of the Earth
By: Schimmel, Schim
Dear Children of the Earth,
I am writing this letter to ask for help. Do you know who I am? I am the planet earth. But I am
much more than just a planet I am your Home. I am your M
Quiz#118892 BL:3.1 PTS:0.5
Josephine Wants to Dance
By: French, Jackie
Josephine loved to dance. Josephine lived in Australia, where she bounced with the
brolgasand leaped with the lyrebirds. The emus showed her how to point her toes. The
eagles taught he
Quiz #101535 BL:4.0 PTS:0.5
The Little Fir Tree
A little fir tree stood by the edge of a forest, a little way off from
the great green trees. It had been a windy day the day the little fir
tree was a seed, and he had blown through the air, out of the
fore
Quiz # 9975 BL: 3.6 PTS: 0.5
Miss Tizzy
Miss Tizzys house was pink and sat like a fat blossom in the
middle of a street with white houses, white fences, and very
neat flower gardens. Miss Tizzy had no fence at all but she had
flowers that grew everywhere
Quiz# 133355 BL: 4.1 PTS:0.514 COWS FOR AMERICA
BY: Carmen Agra Deedy
The remote village waits for a story to be told. News travels
slowly to the corner of Kenya. As Kimeli nears his village, he
watches a herd of bull giraffes cross the open grassland. He
Quiz # 131872 BL: 4.8 Pts: 0.5 Nubs The True Story of a Mutt, a Marine & a Miracle
Outside a border fort in the desert of western Iraq, a small, thin dog
watched and waited. His ears had been cut off to make him a dog of war. He
had no name, and no person
Quiz#111592 Bl:3.0 Pts:0.5
Panda Whispers
In the treetops, by the river, on
the mountains, plains, and sea,
creatures settle down to sleep
and dream sweet dreams, like
you and me.
On a mountain, mist is settling.
Panda cuddles with her cub.
Pointing to th
Quiz # 119841 BL:3.3 Pts:0.5
Anderson, Jamson
LOTUS
By:
Its the day of a huge car show. A shiny sports car rolls into the
parking lot. The sleek look of the Lotus wows everyone who sees it.
Colin Chapman built the first Lotus model in 1948. It was called
Objectives
Introduce financial accounting, its uses, and the primary financial statements
Review debit/credit conventions
Define assets, liabilities and equity
Provide overview of balance sheet content
Introduce common balance sheet ratios
Define re
HUM 2223: Renaissance to Modern
Exam 1 Study Guide
K. Saffle
Directions: Use the following terms to prepare for the exam. This is not a required assignment.
GENERAL: DATES TO KNOW
All major historical periods (Ex: The High Renaissance)
All art listed un
Business Calculus
Final Exam Review 2016
Name:
1. Be able to interpret a graph’s limits and be able to identify values on a gTaph just by looking at it.
2. Evaluate the limits below. (Make sure you Show your work! E)
(a) lim (33¢2 a 3x + 4.)
36-3-2
: 35(
Business Calculus
Exam 1 Review Spring 2016
1. Be able to interpret graphs like examples 1—12 and 29—34 in 11.2 of your book;
i
2. Evaluate the limits below.
a. lim (6x2—2x+3)
JC—)—3 |‘\'\ \“S4
{9 \Ymmtotl lint—l l 11(20th 60195 we a J l)
D
50, W (tx'hzw
Exam 2 Review
Business Caiculus
1. Find the derivative
(8) f(x) =3?“1 (b) y =1n(2—5x2)
ii; A” - e. m
mo“) AX Z’SXZ X
;
L 40%)
QXH ﬂ I - C
Z~Sx
w ‘ WA}
~ lie I [OK
F We
’ a - 3x1
2. Let f(x) = lenx. 3. Consider the function f(x) = 2x3 + 3x2 — 12x +1.
(3)
MATH 2144 Simmons
2.7: Limits at Infinity
So far weve been considering limits as , where is a finite number, but what
if we wanted to determine the long term behavior of a function?
Notation:
;
increases without bound.
;
decreases without bound.
Examp
MATH 2144 Simmons
2.6: Trigonometric Limits
Important Trigonometric Limits:
sin
=
0
1 cos
=
0
lim
lim
Recall from 2.2: lim 0
Example 1: Evaluate lim 0
sin
3
sin
=
.
2.6 - Page 1 of 6
MATH 2144 Simmons
Example 2: Evaluate lim 0
sin 7
7
.
WARNING! The t
MATH 2144 Simmons
2.8: Intermediate Value Theorem
Consider the following two cases:
A hiker spends 3 days hiking up
Mount Kilimanjaro, which has an
elevation of 5895 meters.
Can we guarantee that at some point in his 3 day journey, the hiker was at an
ele
MATH 2144 Simmons
2.4: Limits and Continuity
Continuous: continuing without stopping: happening or existing
without a break or interruption.
The following are graphs of continuous functions;
while these are examples of discontinuous functions.
Question: W
MATH 2144 Simmons
Precalculus Review: Inverse Functions
Section 1.5
Informally the inverse of (), denoted 1 (), is the function that reverses the
effect of ().
Look at inputs and outputs of two related functions:
g ( x)
f ( x) 3 4 x
x 3
4
Input x
f(x)
Ou
MATH 2144 Simmons
2.2: Limits: A Numerical and Graphical Approach
When the values successively attributed to the same variable
approach a fixed value indefinitely, in such a way as to end up
differing from it by as little as one could wish, this last valu