Assignment_2 - Assignment 2 Calculus I with Review Math 150...

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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 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 ent com m 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 com 1 men t 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 typ e yfi nal 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 typ e yfi nal stud 2 2 stud 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 yM T 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 yM T 22 22 2 2 2 2 2 2 2 22 22 22 22 22 22 22 22 22 22 2 stud 22 22 2 2 2 2 2 2 2 22 22 22 22 22 22 22 22 22 22 2 stud corr e ct corr ed ecte d che ck che ed cked don 5 13 13 16 St. 5.1 16 St. 1.5 17 19 19 20 25 2 96 16 12 26 17 St. 1.6 35 22 48 29 St. 5.2 34 63 Ch.3 738 42 Eb. p.133 10 45 12ace 349 St. 2.1 659 8 don e e uestio st ion n que q ion sect t seext ctio 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 right-hand Riemann sums RE RE identifying one-to-one 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 one-to-one 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 one-to-one 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 . 2 2 2 2 2 (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. 2 2 2 done 2 checked 2 corrected 2 2 2 study MT 2 study final 2 Extra-Practice Questions: Try these questions for some more practice. The more practice you get the better you will Extra-Practice 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.

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