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School: Air Force Academy
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School: Air Force Academy
2002 D.W.MacLean: Techniques for Finding Derivatives-1 Techniques for Finding Derivatives The following rules will (mostly) be proved in the section on Rigorous Derivatives. Our purpose now is to learn them, and to learn how to use them. As usual, i
School: Air Force Academy
2002 D.W.MacLean: Rigorous Treatment of Limits-1 Rigorous Treatment of Limits So as to keep things as simple as possible, we begin with the theory of right-hand limits. The theory of left-hand limits is equivalent when appropriately formulated. The
School: Air Force Academy
Graphs of Functions 1 iversitas Un DEO ET PATRI Graphs of Functions Before the development of graphing calculators and personal computers it was often necessary to manually compute and graph functions. In order to do this, one needed a fundamental
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Graphs of Rational Functions 1 Sa iversitas Un DEO PATRI ET Sketching Rational Functions Recall that a rational function f (x) is the quotient of two polynomials: f (x) = p(x) . Things would be simpler if we q(x) could assume that p and q had no c
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Graphs of Trigonometric Functions 1 Sa iversitas Un DEO PATRI ET Sketching Combinations of Trigonometric Functions Note: For most problems, the graph can be viewed interactively using Java applets with Netscape Communicator or Internet Explorer. C
School: Air Force Academy
Math 100.6: Mathematics for Education Students Course Information Term: Lectures: Lecture Location: Term 1-2009 Spring & Summer Session Monday-Friday: 8:30 a.m. to 10:50 a.m. EDUC 1022 Contact Information Instructor: Email: Website: Office Hours: Of
School: Air Force Academy
1 Tests for Divisibility, Theorems for Divisibility, the Prime Factor Test Definition: Prime numbers are numbers with only two factors, one and itself. For example: 2, 3, and 5. Definition: Composite numbers are counting numbers that have more than
School: Air Force Academy
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School: Air Force Academy
University of Saskatchewan Department of Mathematics & Statistics Arts & Science MATH 110.3 Section 97 Course Outline for September to December 2008 Lectures: Tue: 10:30am 11:50am, Thu: 4:00pm-5:20pm Labs: Tue: TBA Note: Students are required to regi
School: Air Force Academy
Math 100.6: Mathematics for Education Students Course Information Term: Lectures: Room: 2007 08 Regular Term Thursday: 10:00 a.m. to 12:50 p.m. TBA Contact Information Instructor: Email: Website: Office Hours: Office Location: Mr. Michael Szafron s
School: Air Force Academy
Section 3-4: Present Value of an Ordinary Annuity PV= PMT [ 1-(1 + i)n] i Where: PV= Present Value PMT= Periodic Payment i = interest rate per period n = number of periods Formula: In an annuity, payments are being made over time. Therefore it is imp
School: Air Force Academy
Inverse Trigonometric Functions The trigonometric functions are not one-to-one. By restricting their domains, we can construct one to-one functions from them. For example, if we restrict the domain of sin x to the interval , 2 2 1 inv we have a one
School: Air Force Academy
Name: S.N.: St. Peter's College MATH 110.3: Calculus I Instructor: M. Szafron Test #1 (90 minutes) September 30, 2003 1. 2. 3. Calculators MAY NOT be used to assist you during this quiz. Cheating on an examination is considered a serious offenc
School: Air Force Academy
Name: S.N.: St. Peter's College MATH 110.3: Calculus I Instructor: M. Szafron Test #2 (90 minutes) October 30, 2003 1. 2. 3. Calculators MAY NOT be used to assist you during this quiz. Cheating on an examination is considered a serious offence
School: Air Force Academy
MATH 110.3 (07) T1, 200506: CALCULUS I Quiz Nine November 17, 2005 40 Minutes No books, notes or calculators are allowed. Show all your work. You must demonstrate you know the procedure used to obtain an answer to a particular problem. Keep the que
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MATH124 CALCULUS I1 for Ellgllleers Lab Section: Quiz 8 (12 pts) Please print names and IDs in ink: Fanlily N a r n r : March 19, 2008 I First Name: I NSlD: S t u d e n t ID: INSTRUCTIONS: 1. Time Limit: 30 minutes 2 No cheating. 3. Closed
School: Air Force Academy
MATH 110.3 (27) T1, 200506: CALCULUS I Test One October 18, 2005 75 Minutes No books, notes or calculators are allowed. There are ten questions; each question is worth ten points. Show all your work. You must demonstrate you know the procedure used
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Instructor: B. Friberg Department of Mathematics & Statistics MATHEMATICS 100.6 (01) TERM TEST #5 Time: 50 min. April 3, 2002 CLOSED BOOK, NO NOTES NO CALCULATORS ALLOWED Properly encode your correct student number and your intended answers on th
School: Air Force Academy
School: Air Force Academy
Solutions to Extra Curve Sketching Problems Sa U versity ni DEO ET PATRIE Section 5.3-39-48 5.3-39 Step 1: f (x) = xex sk atc he w f (x) = (x) ex + x (ex ) = (1)ex + xex = (x + 1)ex and f (x) = (x + 1) ex + (x + 1) (ex ) = (1)ex + (x + 1)ex =
School: Air Force Academy
School: Air Force Academy
School: Air Force Academy
Examples of Log Equation Calculations-II-1 (1) (2) (3) (4) (5) (6) Solve for f if e3t = 2 t f Solution Solve for f if e3t = 2 f t Solution Solve for f if e(ln 3)t = 2 f t Solution Solve for f if e(ln 5)t = 10 t f Solution Solve for f i
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Exercises for Sketching Quartics-1 Exercises for Sketching Quartics Sketch the graphs of: (1) (2) (3) (4) (5) (6) (7) (8) y = f (x) = x 4 2x 3 x 2 + 2x. Solution y = f (x) = x 4 + x 3 x 2. Solution y = f (x) = x 4 8x 2 + 16. Solution y
School: Air Force Academy
Solutions for Lab #5 Section 2 6.2 -6 ln 10 + 1 1 ln 9 = ln 10 + ln 9 2 = ln 10 + ln 3 = ln(10)(3) = ln 30 2 6.2 -8 ln x + a ln y b ln z = ln x + ln y a ln zb = ln xy a zb 6.2 -10 This is the graph of y = ln x (see Figure 4, p.379), plus its re