Calculus II Maple T.A. Course Module
Gord Clement and Jack Weiner, University of Guelph
This course module has been designed to accompany the second semester of the introductory
honours calculus course at the University of Guelph. At Guelph, we have a twelve week
semester, with three fifty minute classes and a fifty minute lab each week.
This is a theoretical course intended primarily for students who need or expect to pursue further
studies in mathematics, physics, chemistry, engineering, or computer science. It is a continuation
of the first semester course Calculus I. These materials have been successfully used with classes
ranging in size from 15 to 600 students.
Topics:
inverse functions
inverse trigonometric functions
hyperbolic functions
L'Hôpital's Rule
techniques of integration
applications of integration to volumes and arc length
parametric equations
polar coordinates
Taylor and MacLaurin series
functions of two or more variables
partial derivatives
The course module consists of 10 question banks and 10 assignments, designed to be used
weekly, beginning in week 2. Almost all questions are algorithmically generated, with
algorithmically generated solutions provided in the question feedback. Over half are Maple
graded.
The tests are presented both as ‘practice’ and as ‘homework’. Students are encouraged to do
practice tests first, where we have configured the tests so that they can check their answers as
they proceed. In the Guelph course, the students are allowed five attempts at the homework quiz,
with only their best mark counting towards their final grade. Each is weighted out of 2%. While
the students do treat these as tests, they really constitute ‘enforced homework’.
The module was first implemented in the Winter, 2007 semester and again in every Winter
semester since. Each time, 500 or more students accessed the tests. After a few coding
adjustments in 2007, the tests have run very smoothly. Incidents where a student insists T.A.
graded a question incorrectly are rare. In each such case, so far, the student has been in error. The
tests are robust.
Following this introduction, you will find
a table of contents for the 10 tests
a T.A. Protocol Sheet
a T.A. Syntax Sheet (We strongly recommend that the students use text rather than
equation editor entry for their answers.)
This course module is copyright Gord Clement, Jack Weiner and Maplesoft. However, you are
welcome to modify and implement the course module at your institution. We encourage you to
send us your suggestions for improvements and/or new questions. If we incorporate any of the
latter, your contribution will be gratefully acknowledged!
Contact Information:
Professor Jack Weiner
Department of Mathematics and Statistics
University of Guelph
Guelph, Ontario, Canada
N1G 2W1
(519) 824-4120, extension 52157
Gord Clement
Westside Secondary School
Orangeville, Ontario, Canada
L9W 5A2
(519) 265-0608
August 22, 2012
Calculus II Maple TA Tests
Prepared by: Professor Jack Weiner ([email protected])
and
Gord Clement ([email protected])
Department of Mathematics and Statistics
University of Guelph
Table of Contents
Test 1: Inverse Functions and Inverse Trig
Test 2: Arctrig Derivatives and Integrals
Test 3: Hyperbolic Trig Functions
Test 4: L’Hôpital’s Rule
Test 5: Integration by Parts and Trig Products
Test 6: Integration by Trig Substitution
Test 7: Integration by Partial Fractions & Improper Integrals
Test 8: Volumes of Revolution & Arc Length
Test 9: Parametric Equations
Test 10: Polar Coordinates
TA PROTOCOL
PLEASE FOLLOW THIS TA PROTOCOL!
1) Work through the sample TA test in your course manual.
2) Do a couple of "Practice" tests. Use "How did I do?" to check your answers on the go. Use "Preview" to check your syntax.
Note: Preview does not recognize interval notation. So don't use preview to check questions requiring aninterval.
Hint: If the answer involves "complicated" math, enter it in Maple, then copy and paste this into TA. TAwill translate your answer into correct syntax. Neat. Please don't abuse this suggestion by getting Maple to DO the questions for you. By all means, use Maple to check your answers.
3) Now you are ready for prime time. You should be able to get perfect on a "Homework" quiz in one or two attempts. You will allowed FIVE attempts. Only your BEST mark will count on TA.
4) DO NOT LEAVE TA TILL THE LAST DAY THE QUIZ IS OPEN!
5) ALWAYS GRADE YOUR TEST WHEN YOU ARE FINISHED. If you didn't do all questions when you grade, TA will inform you. Then you MUST click grade again. If you click, "View Details", you will see your entire test and be given the option of printing it.
6) Always "QUIT AND SAVE" after you finish a test whether it is homework or practice.
All your homework tests are saved in the system and you can retrieve and view them at any time.
Unless indicated otherwise in class, do NOT switch math entry mode to symbolic math. Continue to use text entry.
Always include arithmetic operations. For example, don't enter xy when you mean x*y. (TA and Maple will treat xy as a single symbol.) Use brackets generously but only and unless otherwise specified in the insructions to a question. Please pay attention to those extra instructions when they are included.
TA SYNTAX (Keep this sheet with you whenever you work on at TA test.)
Math Expression TA text entry syntax
x*y; x/y
x^y
a/(b*c) or TA likes a/b/c (but I don't)
sqrt(x) or x^(1/2) Do not use x^.5!
x^(2/3)
abs(x)
ln(x); log[2](x)
; ; exp(x); e or exp(1); pi or Pi; infinity
sin(x)^2 or (sin(x))^2
TA always uses 1+ tan(x)^2 for sec(x)^2 but sec(x)^2 is fine.
TA always uses 1+ cot(x)^2 for csc(x)^2 but csc(x)^2 is fine.
TA always uses sin(x)/cos(x)^2 for sec(x)*tan(x) but sec(x)*tan(x) is fine.
TA always uses cos(x)/sin(x)^2 for csc(x)*cot(x) but csc(x)*cot(x) is fine.
Test 1: Inverse Functions and Inverse Trig
Question 1: Score 1/1
For a function to have an inverse, it must be
Correct
Your Answer: one to one
Comment:
Question 2: Score 1/1
Correct
Your Answer:
Comment: Interchange and and solve.
Question 3: Score 1/1
State the exact value of arccot . Give your answer in radian measure. Use Pi or pi for . Correct
Your Answer: 1/6*Pi
Comment: Remember arccot has range .
Question 4: Score 1/1
Find the domain of the function ( ). Correct
Your Answer:
Comment: arcsec is undefined for
arcsec is undefined for
Question 5: Score 1/1
Correct
Your Answer:
Comment:
Question 6: Score 1/1
Correct
Your Answer: -1.4
Comment:
Question 7: Score 1/1
Correct
Your Answer: 4/9*Pi
Comment: Remember arccsc has range .
Question 8: Score 1/1
Correct
Your Answer: 1/6*Pi
Comment: Remember arctan has range .
Question 9: Score 1/1
Correct
Your Answer: Does not exist!
Comment: -0.5 is not in the domain of arcsec.
Question 10: Score 1/1
Find the exact value of .
Correct
Your
Answer:
Comment: Remember that arccos has range . This means that the triangle you draw should be in the first or second
quadrant, use the CAST rule to determine which.
Question 11: Score 1/1
Find the exact value of
Correct
Your Answer:
Comment:
arccos
In this picture , by the Pythagorean Theorem .
From here , .
In this picture , , by the Pythagorean Theorem .
From this we see , .
Now we just need to use the formula
Question 12: Score 1/1
Complete the square: Correct
Your Answer:
Comment:
Test 2: Arctrig Derivatives and Integrals
Question 1: Score 1/1
Find the derivative:
Correct
Your Answer:
Comment:
Question 2: Score 1/1
Find the derivative:
Correct
Your Answer:
Comment:
Question 3: Score 1/1
Correct
Your Answer:
Comment:
Question 4: Score 1/1
Correct
Your Answer:
Comment:
Question 5: Score 1/1
Correct
Your Answer: (64-25*x^2)^(1/2)+1/5*arcsin(5/8*x)+C
Comment:
Question 6: Score 1/1
Correct
Your Answer: -1/2*ln(81+25*x^2)+1/45*arctan(5/9*x)+C
Comment:
Question 7: Score 1/1
Correct
Your Answer: 2/3*ln(3*x^2-24*x+49)+17/3*3^(1/2)*arctan((x-4)*3^(1/2))+C
Comment:
Question 8: Score 1/1
Correct
Your Answer: -2*(7-2*x^2-4*x)^(1/2)-3*2^(1/2)*arcsin(1/3*2^(1/2)*(x+1))+C
Test 3: Hyperbolic Trig Functions
Question 1: Score 1/1
Algebraically, Using this,
Correct
Your Answer:
Comment:
Question 2: Score 1/1
Which of the following is the graph of y= ? Correct
Your Answer:
Comment:
Question 3: Score 1/1
Find the derivative:
Correct
Your Answer:
Comment: Remember + + + - - -
Question 4: Score 1/1
Find the derivative:
Correct
Your Answer:
Comment: Remember + + + - - -
Question 5: Score 1/1
Find the derivative:
Correct
Your Answer:
Comment: Remember + + + - - -
Question 6: Score 1/1
Remember that If 9 then Correct
Your Answer:
Comment:
Question 7: Score 1/1
Find the integral:
Correct
Your Answer:
Comment: Remember + + + - - -
Question 8: Score 1/1
Find the integral:
Correct
Your Answer:
Comment: Remember + + + - - -
Question 9: Score 1/1
Find the integral:
Correct
Your Answer:
Comment:
Question 10: Score 1/1
Which of the following is the graph of y=arccosh(x)?
Correct
Your Answer:
Comment:
Question 11: Score 1/1
Correct
Your Answer:
Comment:
Question 12: Score 1/1
BABA works for archyperbolics!
Correct
Your Answer:
Comment:
Test 4: L’Hôpital’s Rule
Question 1: Score 1/1
Which of the following (there may be more than one!) are indeterminate forms?
Choice Selected
`1^infinity` Yes [answer withheld]
`infinity/0` No [answer withheld]
`0/0` Yes [answer withheld]
`0^1` No [answer withheld]
Correct
Number of available correct choices: 2
Question 2: Score 1/1
Which of the following conditions form the HYPOTHESIS for the basic form of L'Hopital's Rule?
Let f and g be functions defined on an open interval containing such that
(i)
(ii) and exist on
(iii) for
(iv) for
(v) exists
(vi)
Correct
Your Answer: (i), (ii), (iii), (v)
Comment:
Question 3: Score 1/1
Correct
Your Answer: -1/3
Comment: This " " limit is set up perfectly for L'Hopital's Rule.
Question 4: Score 1/1
Correct
Your Answer: 1/2
Comment:
" "
= by L'Hopital's Rule
=
Question 5: Score 1/1
Correct
Your Answer: 1/2
Comment:
" "
= "0/0" by L'Hopital's Rule
= by L'Hopital's Rule =
Question 6: Score 1/1
Correct
Your Answer: 1
Comment:
" "
= by L'Hopital's Rule
=
Question 7: Score 1/1
Correct
Your Answer: 2
Comment:
" "
= "0/0" by L'Hopital's Rule
= by L'Hopitals Rule
=
Question 8: Score 1/1
Correct
Your Answer: 1/2
Comment: Make a common denominator to combine the fractions, then use L'Hopital's Rule
Question 9: Score 1/1
Evaluate:
Correct
Your Answer: -1/5
Comment: This is the indeterminant form .Start this question by dividing top and bottom by .
Question 10: Score 1/1
Evaluate:
Hint: When
Correct
Your Answer: -1/5
Comment: This is the indeterminant form " ". To start this question divide top and bottom by .
Question 11: Score 1/1
Correct
Your Answer: 1
Comment:
" "
= " "
= by L'Hopital's Rules
=
Question 12: Score 1/1
Correct
Your Answer: e^-28
Comment:
" "
= " "
= by L'Hopital's Rule
=
Question 13: Score 1/1
Correct
Your
Answer: infinity
Comment: If your answer is correct, GOOD!If you applied L'Hopital's Rule here, you probably got the wrong answer. This
question does NOT involve an indeterminate form. BE CAREFUL!
Test 5: Integration by Parts and Trig Products
Question 1: Score 1/1
Find
Correct
Your Answer: 1/4*cos(2*x)+1/2*x*sin(2*x)+C
Comment:
Let
Question 2: Score 1/1
Find
Hint: Remember .
Correct
Your Answer: -1/2*x*cot(2*x)+1/4*ln(abs(sin(2*x)))+C
Comment:
Let
Question 3: Score 1/1
Find .
Hint: Let so that Substitute and use Integration by Parts on the resulting integral.
Correct
Your Answer: 2*cos(x^(1/2))+2*x^(1/2)*sin(x^(1/2))+C
Comment:
Let
Let
Question 4: Score 1/1
Correct
Your Answer:
Comment:
Question 5: Score 1/1
Correct
Your Answer:
Comment:
Question 6: Score 1/1
Evaluate .
Correct
Your Answer: 1/10*(-1+x^10)*exp(x^10+3)+C
Comment:
Let
Question 7: Score 1/1
Evaluate
Correct
Your Answer: -1/10*x^10*cos(x^10+3)+1/10*sin(x^10+3)+C
Comment:
Let
=
Question 8: Score 1/1
Evaluate . Don't forget absolute value where it is needed.
Correct
Your Answer: 1/2*sec(x)*tan(x)+1/2*ln(abs(sec(x)+tan(x)))+C
Comment:
Let
Question 9: Score 1/1
Correct
Your Answer:
Comment:
Question 10: Score 1/1
Correct
Your
Answer:
Comment: The question asked for the BEST strategy. If you let , you will end up with a question that
requires . You know the integral of and you can now use I by P to
integrate . This works but is two steps longer than the BEST strategy, which is to use I by P right away.
Question 11: Score 1/1
Correct
Your Answer:
Comment:
Question 12: Score 1/1
Correct
Your Answer:
Comment:
Question 13: Score 1/1
Correct
Your Answer: 1/2*x+1/16*sin(8*x)+C
Comment:
=
=
Test 6: Integration by Trig Substitution
Question 1: Score 1/1
An integral involves If you solve it by trigonometric substitution, you set Correct
Your Answer:
Comment:
Question 2: Score 1/1
Correct
Your Answer:
Comment:
Question 3: Score 1/1
Correct
Your Answer:
Comment:
Question 4: Score 1/1
An integral involves a power of the expression . After completing the square, we
would use the trigonometric substitution Correct
Your Answer:
Comment: After completing the square we have a power of .
Question 5: Score 1/1
An integral involves a power of the expression . After completing the square, we would
use the trigonometric substitution Correct
Your Answer:
Comment: After completing the square we have a power of .
Question 6: Score 1/1
Evaluate dx.
Correct
Your Answer: -((1-9*x^2)^(1/2)+3*arcsin(3*x)*x)/x+C
Comment:
Let .
therefore and
, Note for therefore .
Where and
Therefore, in both cases
Question 7: Score 1/1
Evaluate dx.
Correct
Your Answer: -(-x+arcsin(x)*(1-x^2)^(1/2))/(1-x^2)^(1/2)+C
Comment:
Let .
therefore and
, Note for therefore .
Where and
Therefore, in both cases
Question 8: Score 1/1
Evaluate dx.
Correct
Your Answer: 1/(1+9*x^2)^(1/2)*x+C
Comment:
Question 9: Score 1/1
Evaluate dx.
Correct
Your Answer: 1/108*(6*x+9*arctan(2/3*x)+4*arctan(2/3*x)*x^2)/(9+4*x^2)+C
Comment:
Let
Where
In both cases,
Question 10: Score 1/1
Evaluate assuming
Hint: Since only use the second quadrant triangle. Don't use absolute value anywhere in
your answer. When , and
so
Correct
Your Answer: -ln((x^2-1)^(1/2)-x)+C
Comment:
Let , Note: since we only use the second quadrant.
Note: for
Test 7: Integration by Partial Fractions & Improper Integrals
Question 1: Score 1/1
As a partial fraction decomposition, we set equal to
Correct
Your Answer:
Comment:
Question 2: Score 1/1
As a partial fraction decomposition, we set equal to
Correct
Your Answer:
Comment:
Question 3: Score 1/1
As a partial fraction decomposition, we set equal to
Correct
Your Answer:
Comment:
Question 4: Score 1/1
True or False: When evaluating the following integral using Partial Fractions, you must first divide the
bottom into the top. dx Correct
Your Answer: False
Comment:
Question 5: Score 1/1
Evaluate dx.
Correct
Your Answer: 11/20*ln(abs(x-3))-9/5*ln(abs(x+2))+5/4*ln(abs(x+1))+C
Comment:
Let
for all
Set :
Set :
Set :
Now
=
Question 6: Score 1/1
Evaluate dx. Correct
Your Answer: x-13/6*ln(abs(x+3))+7/6*ln(abs(x-3))+C
Comment:
After performing long division,
Let
Set :
Set
Now,
Question 7: Score 1/1
Evaluate dx.
Correct
Your Answer: 1/5*arctan(1/2*x)+1/5*ln(x^2+4)+3/5*ln(abs(x-1))+C
Comment:
Let
=
Set :
Coefficient of
Coefficient of :
Therefore,
=
Question 8: Score 1/1
Evaluate the improper integral: dx. Your answer should be a finite number,
infinity, -infinity, or enter DNE if it does not exist. Start this problem by rewriting the improper integral
as the limit of a proper integral.
Correct
Your Answer: DNE
Comment:
dx
=
=
=
Therefore the integral does not exist.
Question 9: Score 1/1
Evaluate dx. Your answer should be a finite number, infinity, -infinity, or enter DNE if
it does not exist. Start this problem by rewriting the improper integral as a limit of a proper integral.
Correct
Your Answer: -infinity
Comment:
=
Question 10: Score 1/1
Evaluate dx. Your answer should be a finite number, infinity, -infinity, or enter DNE if
it does not exist. Start this problem by rewriting the improper integral as a limit of a proper integral.
Correct
Your Answer: 7
Comment:
Question 11: Score 1/1
Evaluate dx. Your answer should be a finite number, infinity, -infinity, or enter
DNE if it does not exist. Start this problem by rewriting the improper integral as a limit of a proper
integral.
Hint: Remember BABA and the Chain Rule in Reverse:
Correct
Your Answer: 1/12*Pi
Comment:
Question 12: Score 1/1
Evaluate the improper integral dx. Your answer should be a finite number, infinity,
-infinity, or enter DNE if it does not exist. Start this problem by rewriting the improper integral as the
limit of a proper integral.
Correct
Your Answer: 2
Comment:
=
=
Test 8: Volumes of Revolution & Arc Length
Question 1: Score 1/1
The integral using vertical rectangles which finds the volume obtained when the region bounded
by and is rotated about the line -4 is given by
Correct
Your Answer:
Comment:
This is a shell.
thickness
Question 2: Score 1/1
The integral using vertical rectangles which finds the volume obtained when the region bounded
by and is rotated about the line -3 is given by
Correct
Your Answer:
Comment:
This is a difference of discs.
Question 3: Score 1/1
The integral using horizontal rectangles which finds the volume obtained when the region bound
by and is rotated about the line -4 is given by
Correct
Your Answer:
Comment:
This is a difference of discs.
Question 4: Score 1/1
The integral using horizontal rectangles which finds the volume obtained when the region bounded
by and is rotated about the line 1 is given by
Correct
Your Answer:
Comment:
This is a shell.
thickness =
Question 5: Score 1/1
By rotating the semi-circle about the axis, we can find the volume of a sphere of
radius 2. The integral which gives this volume is
Correct
Your Answer:
Comment:
This is a disc.
Question 6: Score 1/1
By rotating the line about the axis from to 2, we can find the volume of a
cone of radius 2 and height 1. The integral using vertical rectangles which gives this volume is
Correct
Your Answer:
Comment:
This is a shell
thickness
Question 7: Score 1/1
By rotating the line about the axis from to 2, we can find the volume of a
cone of radius 5 and height 2. The integral using horizontal rectangles which gives this volume is
Correct
Your Answer:
Comment:
This is a disc.
Question 9: Score 1/1
. Give your answer to TWO decimal places.
(HINTS: The integral you will have to evaluate is NOT HARD. To get your approximation, work out
your answer exactly using THE Fundamental Theorem of Calculus--F(b)-F(a)--and then go to Maple and
use "evalf(F(b)-F(a))".)
Correct
Your Answer: 7.8466
Comment: Arclength
Question 10: Score 1/1
Correct
Your
Answer:
Comment: How would you modify this integral so that you would find the length of the upper half of the ellipse
x^2/a^2+y^2/b^2=1?
Test 9: Parametric Equations
Question 1: Score 1/1
Which of the following pairs of parametric equations draws the circle of radius 6 from (6, 0) counter-
clockwise to (0,-6)?
Correct
Your Answer:
Comment:
Question 2: Score 1/1
Find , where and .
Correct
Your Answer: -1/16*(sin(3*t)*t+cos(3*t))/t^7
Comment:
=
=
=
Question 3: Score 1/1
Find dy/dx where and . Correct
Your Answer: 4*cos(4*t)/(4+4*tan(4*t)^2)
Comment:
Question 4: Score 1/1
Which of the following pairs of parameric equations draws the ellipse
clockwise from (0, -3) to (7,0)?
Correct
Your Answer:
Comment:
Question 5: Score 1/1
State the intercept(s) using set notation, that is, { }, for the parametric equations
and .
(Some answers involve "ln". Don't use absolute value signs in your answer if they are not necessary. Use
exp(x) for )
Correct
Your Answer: {-sin(9), sin(3)}
Comment:
To find intercepts, set and solve.
therefore or .
Corresponding to we have intercept -sin(9).
Corresponding to we have intercept sin(3).
Enter your answer as
{-sin(9), sin(3)}
Question 6: Score 1/1
State the intercept(s) using set notation, that is, { }, for the parametric equations
and .
(Some questions involve "ln". Don't use absolute value if it is not necessary. Remember to use exp(x)
for )
Correct
Your Answer: {49, 64}
Comment:
To find y intercepts, set and solve.
=
Therefore or
Corresponding to we have y intercept 64.
Corresponding to we have y intercept 49.
Enter your answer as {64, 49}.
Question 7: Score 1/1
A pair of parametric equations is defined for all real numbers . The first derivative is given
by . For what intervals is the graph INCREASING, that is,
when is increasing as increases?
Note/Hint: A function can still be increasing on an interval even if its derivative is 0 or undefined
somewhere in the interval!
Correct
Your Answer:
Comment:
Question 8: Score 1/1
A pair of parametric equations using parameter is defined for The first derivative is given
by . At and , we have Correct
Your Answer:
Comment:
Horizontal tangents occur when .
Question 9: Score 1/1
A pair of parametric equations using parameter is defined for The first derivative is given
by . At , we have Correct
Your Answer:
Comment:
Vertical tangents occur when .
Question 10: Score 1/1
Vertical asymptotes are finite values, that is , where approaches either plus or minus
infinity.
List in set notation, that is, { }, the value(s) of for the relation given by
and .
Correct
Your Answer: {0, 1/8}
Comment:
Therefore is a vertical asymptote.
Therefore is a vertical asymptote.
Enter your answer as {0, 1/8}.
Question 11: Score 1/1
Horizontal asymptotes are finite values, that is , where approaches either plus or minus
infinity.
List in set notation, that is, { }, the value(s) of for the relation given by
and .
Correct
Your Answer: {2}
Comment:
Therefore is a vertical asymptote.
never tends to , therefore this is our only vertical asymptote.
Enter your answer as {2}.
Question 12: Score 1/1
A pair of parametric equations is defined for all real numbers The second derivative is given
by . For what intervals is the graph concave down?
Note/Hint: A function can still be concave down on an interval even if its second derivative is 0 or
undefined somewhere in the interval!
Correct
Your Answer:
Comment:
Test 10: Polar Coordinates
Question 1: Score 1/1
The rectangular coordinates corresponding to polar coordinates ( , ) are
Correct
Your Answer: ( , )
Comment:
Question 2: Score 1/1
One pair of polar coordinates corresponding to rectangular coordinates ( , ) are
Correct
Your Answer: ( , )
Comment:
Since , is in the 3rd quadrant, choose ,
therefore one name for the point in polar coordinates is ,
Question 3: Score 1/1
Which of the following gives all possible coordinates of polar coordinates ( , )?
Correct
Your Answer: ( , ) and ( , )
Comment:
Question 4: Score 1/1
Two of the following polar equations generate this graph. Which?
Choice Selected
No [answer withheld]
No [answer withheld]
Yes [answer withheld]
Yes [answer withheld]
Correct
Number of available correct choices: 2
Partial Grading Explained
Comment:
Question 5: Score 1/1
Two of the following polar equations generate this graph. Which?
Choice Selected
No [answer withheld]
No [answer withheld]
Yes [answer withheld]
Yes [answer withheld]
Correct
Number of available correct choices: 2
Partial Grading Explained
Comment:
Question 6: Score 1/1
Two of the following polar equations generate this graph. Which?
Choice Selected
No [answer withheld]
Yes [answer withheld]
Yes [answer withheld]
No [answer withheld]
Correct
Number of available correct choices: 2
Partial Grading Explained
Comment:
Question 7: Score 1/1
Two of the following polar equations generate this graph. Which?
Choice Selected
Yes [answer withheld]
No [answer withheld]
No [answer withheld]
Yes [answer withheld]
Correct
Number of available correct choices: 2
Partial Grading Explained
Comment:
Question 8: Score 1/1
Two of the following polar equations generate this graph. Which?
Choice Selected
No [answer withheld]
Yes [answer withheld]
Yes [answer withheld]
No [answer withheld]
Correct
Number of available correct choices: 2
Partial Grading Explained
Comment:
Question 9: Score 1/1
Two of the following polar equations generate this graph. Which?
Choice Selected
No [answer withheld]
Yes [answer withheld]
Yes [answer withheld]
No [answer withheld]
Correct
Number of available correct choices: 2
Partial Grading Explained
Comment:
Question 10: Score 1/1
Which of the following polar equations generates this graph?
Correct
Your Answer:
Comment:
Question 11: Score 1/1
Which of the following polar equations generates this graph?
Correct
Your Answer:
Comment: