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Unformatted text preview: Assignment 2
Calculus I with Review
Math 150  D100 (Summer 2011) Assignment 2 Quiz date: Tuesday, May 24 Complete this assignment by Wednesday in your I with journal. This will give you plenty of time to make sure you
Calculus homework Review
understand the material before the quiz at the end of Friday’s class. Quiz questions will be taken from the textbook
Math 150  D400 (Spring 2010)
questions listed below or the additional questions on page 2.
Some suggestions for using your homework journal are: Quiz date: Friday, January 22, 2010 • Do rough work on scratch paper.
• If you ﬁnd one solution, try to ﬁnd another (a simpler solution may reveal itself). Complete this assignment by Tuesday in your whole without all theThis will give you plenty of time
• When you ﬁnd a solution, try to see it as a homework journal. little details.
to make questions in order and the materialquestionthe quiz at the end of Friday’s class.
• Do sure you understand clearly label before and section numbers.
•Some suggestionsassignment your homeworkare posted. Catch your mistakes now when the stakes are low rather
Grade your own for using when solutions journal are:
than making them on exams. • Do rough work on scratch paper.
• If maximum marks on the quiz, ﬁnd another (a simpler solution may reveal itself).
To obtain you ﬁnd one solution, try to your answer should be in a form that another student could understand without
• When poorly expressed but correct result is whole cient.
undue eﬀort: ayou ﬁnd a solution, try to see it as anot suﬃwithout all the little details.
• Do questions in order and clearly label question and section numbers.
• Grade your own assignment when solutions are posted. Catch your mistakes now when the
stakes are low rather than making them on exams.
1. Online Questions: (from LONCAPA: https://loncapa.sfu.ca):
To obtain maximum marks on the quiz, your answer should be in a form that another student could
Questions in folders: 5.1, 5.2 understand without undue eﬀort: a poorly expressed but correct result is not suﬃcient. 1 1 2
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n text 2. Questions from textbook:
Questions from textbook(s): CD RE transformations of ex
using Riemann sums to estimate area
CD RE ﬁnding domains
using Riemann sums from a table of values
CD the distance problem from a graph
CE families (i.e. ”types”) of functions
CD expressing area as a limit
RE diﬀerence quotient (algebra)
RE deconstructing a limit
WP modeling growth
RE righthand Riemann sums
RE RE identifying onetoone functions
using Riemann sums to estimate area from graph
RE CE Midpoint rule to approximate an integral
the working with inverse functions
CD RE TC: Do limit in under 3 minutes?
recognizing a this as a deﬁnite integral
CD RE TC: Do this in under the deﬁnition
computing an integral from 2 minutes?
CD RE solving equations with exp & log
recognizing a deﬁnite integral as a limit
RE CE facts from basic geometry
use inverse trigonometric functions
RE RE function integral by interpreting as an area
evaluating an domains & simpliﬁcation
CD RE interval integrals
properties of notation
3
RE RE the resultinqualities e3 − e
use solving 1 ex dx =
CD RE use a of integrals or calculator
properties computer
CE use integral properties to estimate value RE
RE use a computer or calculator
use a computer or calculator See the legend on last page of this assignment for what these acronyms mean. See the legend on last page of this assignment for what these acronyms mean.
1 1 Additional questions:
These questions are made up by your instructor and may require a blend of ideas that we
have encountered so far in the course. They are similar to exam style questions in that it
Additional questions: section of the text is directly related to solving the problem. You
is not entirely clear what
These have to decidemade up by your instructorrequired. require a blend of ideas that we
will questions are what tools/techniques are and may
have encountered so far in the course. They are similar to exam style questions in that it
is A1. entirely clear what section of the text is directly related is given by the problem. You
not Let f be a onetoone function whose inverse function to solving the formula
will have to decide what tools/techniques are required.
f −1 (x) = x5 + 2x3 + 3x + 1.
A1. Let f be a onetoone function whose inverse function is given by the formula
(a) Compute f −1 (1) and f (1).
f −1 (x) = x5 + 2x3 + 3x + 1.
(b) Compute the value of x0 such that f (x0 ) = 1.
(a) Compute f −1 (1) and f (1).
(c) Compute the value of y0 such that f −1 (y0 ) = 1.
(b) Compute the value of x01such that f (x0 ) = 1.
(d) Below is a graph of f − . Draw an approximate graph of f .
(c) Compute the value of y0 such that f −1 (y0 ) = 1.
(d) Below is a graph of f −1 . Draw an approximate graph of f . done
2 checked
2 corrected
2 study MT
2 study ﬁnal
2 A1. Suppose the done (1, 2) lies on the graphstudy MT study ﬁnal
point checked corrected of the function f .
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(a) Find a point on the graph of the function g (f (x)), where g (y ) = y − 1 + arctan (y/2).
A1. Suppose the point (1, 2) lies on the graph of the function f .
(b) Find two points on the graph of the function f (h(x)), where h(x) = x2 − π x + cos2 x.
(a) Find a point on the graph of the function g (f (x)), where g (y ) = y − 1 + arctan (y/2).
done checked corrected study MT study ﬁnal 2
(b) Find two points 2 the graph of the 2
on
function f (h(x)), where h(x) = x − π x + cos2 x.
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done
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2 2 2 study MT
2 study ﬁnal
2 ExtraPractice Questions:
Try these questions for some more practice. The more practice you get the better you will
ExtraPractice Questions:
understand the materialsome the better you will do on quizzes and exams. better you will
Try these questions for and more practice. The more practice you get the understand the Section 1.5: 2,the 5, 11, 12, 15, 21, 29 quizzes and exams.
• (Stewart) material and 3, better you will do on
• (Stewart) Section 1.6: 3, 7, 11, 11, 12, 15, 21, 29 47, 61, 65, 67, 71
• (Stewart) Section 1.5: 2, 3, 5, 17, 22, 25, 33, 45,
• (Stewart) Section 2.1: 1, 5, 7 17, 22, 25, 33, 45, 47, 61, 65, 67, 71
• (Stewart) Section 1.6: 3, 7, 11,
• (Ebersole) Section 2.1: (page 7
• (Stewart) Chapter 3: 1, 5, 131) 1, 2, 6; (page 130) 1, 2, 3
• (Ebersole) Chapter 3: (page 131) 1, 2, 6; (page 130) 1, 2, 3 Legend (for ”type” of question):
RE = Routine Exercise: question):
Legend (for ”type” of This is something you should be able to do in your sleep ;). Your
goal is to be able to answer these questions quickly and accurately everyin your These ;). Your
RE = Routine Exercise: This is something you should be able to do time. sleep form the
foundations ofable to answer these questions quickly and accurately every time. These form the
goal is to be your skill set.
TC = Time of your skillThe most important part about solving problems is getting the answer
foundations Challenge: set.
right,= Time Challenge: The most important part about and midterm exams,getting the answer
TC i.e., accuracy. Speed, however, is a factor on quizzes solving problems is and an indication
of how i.e., accuracy. practiced. Try tois a these questions withinmidterm exams, and an5indication
right, well you have Speed, however, do factor on quizzes and the time limit, usually minutes.
If you need more time than that, itsto do these questions within the time limit, usually 5 minutes.
of how well you have practiced. Try o.k., but keep practicing!
WP =need more time than that, its words into expressions (also known as modeling): Master
If you Word Problem: Translating o.k., but keep practicing!
this skill Word we will using this all term.
WP = now, Problem: Translating words into expressions (also known as modeling): Master
CD = Concepts and Deﬁnitions: These questions relate to your understanding of the ”new
this skill now, we will using this all term.
language” we are introducing. They should help you remember theunderstanding of the ”new
CD = Concepts and Deﬁnitions: These questions relate to your important deﬁnitions and
theorems. we are introducing. They should help you remember the important deﬁnitions and
language”
CE = Concepts and Explorations: This indicates a question which is testing your understanding
theorems.
of the fundamentals. It is not a routine exercise since the solution process may not understanding
CE = Concepts and Explorations: This indicates a question which is testing your be obvious at
ﬁrst glance. It may takeis not a routine exerciseto ﬁgure out what to do, don’t be afraid to play
of the fundamentals. It a little bit of thought since the solution process may not be obvious at
around with some ideas. You’ll learnof thought to ﬁgure out what to do, don’t be which lead to
ﬁrst glance. It may take a little bit more by making mistakes and taking routes afraid to play
dead ends. You must be able to do these types making mistakes and taking routes this material.
around with some ideas. You’ll learn more by of questions to succeed in learning which lead to
HL =ends. You must be able to do This indicates a question to succeed in learning this material.
dead Higher Level Understanding: these types of questions which is testing understanding at a
higher level. These questions will require more thought than a RE or FLP so don’t be discouraged
HL = Higher Level Understanding: This indicates a question which is testing understanding at a
if you can’t see how to do this immediately. Perseverance and a RE or FLP so with ideas is the key
higher level. These questions will require more thought than playing around don’t be discouraged
to you can’t see how to do this immediately. Perseverance and an expected outcomeideas is course.
if these questions. Understanding this material at this level is playing around with of this the key
CM = Computer of Computational Device: This this level isaan expected outcome of this course.
to these questions. Understanding this material at indicates question in which a computer or
calculator is needed. Computational Device: This indicates a question in which a computer or
CM = Computer of calculator is needed.
Selected Hints & Answers:
1.6 #16: Don’t try to ﬁnd an expression for f −1 , it would be diﬃcult to do and isn’t needed.
Selected Hints & Answers:
#26: f −1 (x) = ln (x) − ln (1 − 2x) #48: (a) x =1 1 (ln 7 − 3), (b) x = 1 (5 − e−3 )
2
2
1.6 #16: Don’t try to ﬁnd an expression for f − , it would be diﬃcult to do and isn’t needed.
#26: f −1 (x) = ln (x) − ln (1 − 2x) #48: (a) x = 1 (ln 7 − 3), (b) x = 1 (5 − e−3 )
2
2 3 3 ...
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This note was uploaded on 08/10/2011 for the course MATH 150 taught by Professor Mohollund during the Summer '08 term at Simon Fraser.
 Summer '08
 MOHOLLUND
 Calculus

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