653
A circular corral of unit radius is enclosed by a fence; A goat is
49- outside the corral and tied to the fence with a rope of length
. a 7 0 (see gure). What is the area of the region (outside the
corral) that the goat can reach?
51. Isogonal curve
Math 243
Quiz # 4
Name: J Q : ' _
Show All Wok
1. Use the geometric series to nd power series representation for the following functions
and determine the interval of conVer'gence: A A JWi C, KL :3 2 2:71
a) f(x)= :x 45m pcqb W 27? cfw_1 r! a
2
1 . no. - 1 1
. (Mr-r 1 1
' *' .n i 1
I 1;" , f \ A / '
' zg ,r r;- -' r K
j , . 1,; V . . I
Mix/(K.- " r a ' ' I v
. f/ G _:
n ,7 .5" on:
Deflnltlon A plane region D 15 said to be of type 2 1f 1t lies between the graphs of two 1.? 7 /Qg6 / i v
_ conti
1
Math 243
Quiz # 8
Name:_
Show All Work
1.
Sketch the domain for the following functions:
a)
f ( x, y) ln(1 x2 y 2 )
b)
f ( x, y )
1
x y2
2. Sketch the level curves for z x2 y; k =-2, -1, 0, 1, 2
2
3. Evaluate the following limits
a)
b)
x 2 x xy y
( x ,
MATH243_B
Exam 2
Name_
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question
Find the limit.
1)
lim
ln
(x, y) (1, 1)
x+y
xy
1)
Find two paths of approach from which one can conclude that the functi
Math 243
Quiz # 7
Name:_
Show All Work
1.
Describe the surface in R3 that is represented by the equation z = 3
2. Show that the P(4, 5, 2), Q(1, 7, 3), R(2, 4, 5) are vertices of an equilateral triangle.
3. Find the standard form of the equation for the s
SUMMARY OF TESTS FOR SERIES
C011dlthIl(S)
'I 71-: Con: 'tion(s)
0_f_ Convergence '. ofD ergence "
" m hm a ah O - lThis test cannot be used
nth Term 7221 an 90 Lie Show convergence.
Geometric Series 2 ar 0 < M < 1 lrl 2 1 S
MATH243
Exam 1 - Part B (Due Date: Friday October 7, 2016)
Name:_
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1. Which of the following sequences converge and which diverge? For each sequence that
converges, find the limit as n approaches.
1 4n 2
a) an
b) an 1 (1.99)n
2
7 3n
d) an
c
Math 243
Quiz # 4
Name:_
Show All Work
1. Use the geometric series to find power series representation for the following functions
and determine the interval of convergence:
4
a) f ( x)
2 x
b) h( x)
x
1 x2
2. Find the power series representation for the
Math 243
Quiz #5
Name:_
Show All Work
1. Express the point with Cartesian coordinates given as (4, 4) in polar coordinates in
two different ways.
2. Plot the point whose polar coordinates is given as (-5, 3/2). Find the corresponding
rectangular coordinat
Math 243
Review Sheet for Final Exam
Chapter 8
You should be able to:
1. Determine if a sequence converge or diverge (page 440: # 10, 14, 18, 24, 25 (use
Squeeze Theorem for # 25
2. Determine if a series is convergent or divergent (page 449: # 4, 10, 12,
Math 243
Quiz # 6
Name:_
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1. Find the focus and the directrix for the following and then sketch the parabola.
a) y 2 16 x
2. Put the following equation for an ellipse in standard form and then sketch the graph
after listing the foci, length o
Math 243
Quiz # 9
Name:_
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1. If h( x, y ) x sin y y cos x, find the first order and the four second order partial derivatives.
2. Find the equation of the tangent plane to the given surface at the specified point.
z 4 x 6 y x2 y 2 9 , (2, -3,
Math 243
Quiz # 3
Name: _
Show All Work Please
1. Use the ratio test to determine if each of the following series converge or diverge.
(1) n n 2 2n 1
a)
3n
n 0
b)
2n
3
n 1 n
c)
n!
e
n 1
n
2. Use the Root Test to determine if the following series converge
MATH243
Extra Credit Assignment
Name_
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question
Find two paths of approach from which one can conclude that the function has no limit as (x, y) approach
Math 243
Quiz # 1
Name:_
1. List the first 4 terms in each of the following sequence:
2
a) an 5
5
n
b) a1 1, an1 1
1
1 an
2. Which of the following sequences converge and which diverge? For each sequence
that converges, find the limit as n approaches.
Math 243
Quiz # 2
Name:_
1. Which of the following series converge and which diverge? Give reasons for your
answer. If the series converges find its sum.
a)
5
n 1
2
b)
n 1
c)
1 n 1
2
n 1 4
d)
n 1
2. Use the integral test to determine if
3
4
n 1
n
n 1
Math 243
Quiz #10
Name:_
Show All Work
1.
Find and analyze the critical point(s) of the functions
i) f ( x, y) 8x2 4 xy 12 x y 2 7
ii) h( x, y ) xy
1 1
x y
2. Find three positive numbers whose sum is 48 and such that their product is as large as
possible
9-2-11
Objectives (what you should be able to do at the end of the class)
1. Represent functions as words, tables, graphs, and
formulas.
2. Use function notation to evaluate functions and solve
for given outputs.
3. Determine if a relationship is a given
8-31-11
Objectives (what you should be able to do at the end of the class)
1. Describe different types of functions with respect to
how they change over time.
2. Distinguish between different types of functions.
3. Write different types of functions based
MATH113: Williams
Inclass: 8-29-11
Problem #1
After graduation from college, you will probably be looking for a job. Suppose you are offered a
job at a starting salary of $40,000 per year. To strengthen the offer, the company promises annual
raises of $40
9-12-11
Announcements
1. Due to the beating that the Steelers took yesterday, I
have to go to the doctors this afternoon and will miss
my office hours today.
2.
Due to convocation, Wednesdays class meetings will
be on the condensed schedule. The 9:05 clas
9-7-11
ANNOUNCEMENT
You will have a few problems to solve as an assessment
on Friday. You will be able to use your resources, but you
will solve them on your own. This way, I will know who
can do what and can match you up with others
accordingly.
Be sure
9-23-11
Objectives (what you should be able to do at the end of the class)
1. Compare situations involving linear, exponential, and
constant growth.
Terms/Concepts
none
Definition (non-mathematical):
Concavity is the state of being curved.
There are diffe
10-5-11
Announcements
1. We WILL be having class on Friday and we WILL be
doing quite a bit. Class meeting will be cancelled on
two other Fridays throughout the semester (October
21st and November 11th) due to Steve being away at a
conference, and you alr
9-14-11
Announcements
1. Assessment #2 will be due on Monday, September
19th, at the beginning of class.
2. Office hours today are from 11:00 until 12:30.
Objectives (what you should be able to do at the end of the class)
1. Explain the relationships betw
12-9-11
Announcements
1. When you are finished with the exam, please take a copy
of Steves Final Letter. Thank you for being such a
wonderful class!
2. Dont forget to submit the take-home part of the final
exam to Steves office (405 Robinson) by 3:00pm on
10-26-11
Announcements
1. Due to Angie (the SA for the 10:10 class, she holds
hours from 2-4) being out in schools the past two
weeks (and next week), she has not been available.
However, Casey is still there from 4-6. Angie will
return after next week.
2