4.5 SUMMARY OF CURVE SKETCHING. Click here for answers. Click here for solutions. y cos x sin x. x 2 x 3 4. x 1 x y x 3 x

Σχετικά έγγραφα
3.4. Click here for solutions. Click here for answers. CURVE SKETCHING. y cos x sin x. x 1 x 2. x 2 x 3 4 y 1 x 2. x 5 2

4.4. Click here for solutions. Click here for answers. CURVE SKETCHING. y ln x 2 x. y ln 1 x 2. y x 2 e x2. x 1 x 2. x 2 x 3. x 5 2. y x 3.

26 28 Find an equation of the tangent line to the curve at the given point Discuss the curve under the guidelines of Section

AREAS AND LENGTHS IN POLAR COORDINATES. 25. Find the area inside the larger loop and outside the smaller loop

r t te 2t i t Find the derivative of the vector function. 19. r t e t cos t i e t sin t j ln t k Evaluate the integral.

Section 8.3 Trigonometric Equations

Section 8.2 Graphs of Polar Equations

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =?

Chapter 6 BLM Answers

Inverse trigonometric functions & General Solution of Trigonometric Equations

Differentiation exercise show differential equation

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates

Complete Solutions Manual for Calculus of a Single Variable, Volume 1. Calculus ELEVENTH EDITION

Review Exercises for Chapter 7

Principles of Mathematics 12 Answer Key, Contents 185

Mock Exam 7. 1 Hong Kong Educational Publishing Company. Section A 1. Reference: HKDSE Math M Q2 (a) (1 + kx) n 1M + 1A = (1) =

ω = radians per sec, t = 3 sec

Section 9.2 Polar Equations and Graphs

Dynamic types, Lambda calculus machines Section and Practice Problems Apr 21 22, 2016

Fourier Series. MATH 211, Calculus II. J. Robert Buchanan. Spring Department of Mathematics

Trigonometric Formula Sheet

Chapter 7 Analytic Trigonometry

Chapter 7 Transformations of Stress and Strain

Integrals in cylindrical, spherical coordinates (Sect. 15.7)

Section 7.6 Double and Half Angle Formulas

University of Illinois at Urbana-Champaign ECE 310: Digital Signal Processing

Lecture 26: Circular domains

ECE 308 SIGNALS AND SYSTEMS FALL 2017 Answers to selected problems on prior years examinations

Solution to Review Problems for Midterm III

CRASH COURSE IN PRECALCULUS

If we restrict the domain of y = sin x to [ π, π ], the restrict function. y = sin x, π 2 x π 2

PARTIAL NOTES for 6.1 Trigonometric Identities

ΖΕΡΔΑΛΗΣ ΣΩΤΗΡΙΟΣ ΤΟ ΟΥΤΙ ΣΤΗ ΒΕΡΟΙΑ (1922-ΣΗΜΕΡΑ) ΘΕΣΣΑΛΟΝΙΚΗ

If we restrict the domain of y = sin x to [ π 2, π 2

wave energy Superposition of linear plane progressive waves Marine Hydrodynamics Lecture Oblique Plane Waves:

Paper Reference. Paper Reference(s) 6665/01 Edexcel GCE Core Mathematics C3 Advanced. Thursday 11 June 2009 Morning Time: 1 hour 30 minutes

Matrices and Determinants

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1

Solutions to Exercise Sheet 5

Trigonometry 1.TRIGONOMETRIC RATIOS

Answers - Worksheet A ALGEBRA PMT. 1 a = 7 b = 11 c = 1 3. e = 0.1 f = 0.3 g = 2 h = 10 i = 3 j = d = k = 3 1. = 1 or 0.5 l =

Math221: HW# 1 solutions

Equations. BSU Math 275 sec 002,003 Fall 2018 (Ultman) Final Exam Notes 1. du dv. FTLI : f (B) f (A) = f dr. F dr = Green s Theorem : y da

Example Sheet 3 Solutions

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

Pg The perimeter is P = 3x The area of a triangle is. where b is the base, h is the height. In our case b = x, then the area is

D Alembert s Solution to the Wave Equation

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

% APPM$1235$Final$Exam$$Fall$2016$

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr

Section 7.7 Product-to-Sum and Sum-to-Product Formulas

Leaving Certificate Applied Maths Higher Level Answers

Finite Field Problems: Solutions

Lifting Entry (continued)

Numerical Analysis FMN011

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds!

Lifting Entry 2. Basic planar dynamics of motion, again Yet another equilibrium glide Hypersonic phugoid motion MARYLAND U N I V E R S I T Y O F

Spherical Coordinates

Q1a. HeavisideTheta x. Plot f, x, Pi, Pi. Simplify, n Integers

10/3/ revolution = 360 = 2 π radians = = x. 2π = x = 360 = : Measures of Angles and Rotations

CHAPTER 101 FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD

Durbin-Levinson recursive method

1 String with massive end-points

4.4 Superposition of Linear Plane Progressive Waves

Geodesic Equations for the Wormhole Metric

Trigonometry (4A) Trigonometric Identities. Young Won Lim 1/2/15

C.S. 430 Assignment 6, Sample Solutions

The Simply Typed Lambda Calculus

( )( ) ( ) ( )( ) ( )( ) β = Chapter 5 Exercise Problems EX α So 49 β 199 EX EX EX5.4 EX5.5. (a)

Reminders: linear functions

MathCity.org Merging man and maths

Differential equations

Arithmetical applications of lagrangian interpolation. Tanguy Rivoal. Institut Fourier CNRS and Université de Grenoble 1

SPECIAL FUNCTIONS and POLYNOMIALS

*H31123A0228* 1. (a) Find the value of at the point where x = 2 on the curve with equation. y = x 2 (5x 1). (6)

6.003: Signals and Systems. Modulation

Πανεπιστήµιο Κύπρου Πολυτεχνική Σχολή

4.6 Autoregressive Moving Average Model ARMA(1,1)


Sampling Basics (1B) Young Won Lim 9/21/13

Solutions - Chapter 4

10.0 C N = = = electrons C/electron C/electron. ( N m 2 /C 2 )( C) 2 (0.050 m) 2.

6.4 Superposition of Linear Plane Progressive Waves

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:

Linearized Lifting Surface Theory Thin-Wing Theory

Review Test 3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

The Negative Neumann Eigenvalues of Second Order Differential Equation with Two Turning Points

Exercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1.

Similarly, we may define hyperbolic functions cosh α and sinh α from the unit hyperbola

CHAPTER 13 Functions of Several Variables

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1

Homework 3 Solutions

Γραφικά Υπολογιστών: 2D Μετασχηματισμοί (transformations)

Παράγωγος πραγματικής συνάρτησης

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΓΕΩΤΕΧΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΚΑΙ ΔΙΑΧΕΙΡΙΣΗΣ ΠΕΡΙΒΑΛΛΟΝΤΟΣ. Πτυχιακή εργασία

Answers to practice exercises

CHAPTER 70 DOUBLE AND TRIPLE INTEGRALS. 2 is integrated with respect to x between x = 2 and x = 4, with y regarded as a constant

The Pohozaev identity for the fractional Laplacian

Introduction to Time Series Analysis. Lecture 16.

Transcript:

SECTION.5 SUMMARY OF CURVE SKETCHING.5 SUMMARY OF CURVE SKETCHING A Click here for answers. S Click here for solutions. 9. 8 Use the guidelines of this section to sketch the curve. cos sin. 5. 6 8 7. cot.. 9. cos sin. sin cos 5. 6.. sin s cos. sin sin 7. 5. e 6. e 8. 5 9. 7. ln cos 8. ln. 9 9. ln. ln.. ln tan.. s s e. ln. e. s 5. s 9 5. s 6. 5. e 6. e 7. s s 8. 7. e 8. ln s Stewart: Calculus: Earl Transcendentals Seventh Edtion. ISBN: 58979. Cengage Learning. All rights reserved.

SECTION.5 SUMMARY OF CURVE SKETCHING.5 ANSWERS E Click here for eercises. S Click here for solutions.. A. R B. -int. C. None D. None E. Inc. on ; dec. on F. Loc. min. f = loc. 7 ma. f = G. CU on 5 CDon 5 IP 5 7 5. A. { } B. -int. f = C. None D. HA =;VA = = E. Inc. on ;dec.on F. Loc. ma. f = G. CD on ; CUon 9. A.R B. -int.7 C. None D. None E. Inc. on ; dec. on F. Loc. ma. f = 7 loc. min. f = 7 G. CU on CD on. IP 5 6. A. { } B. None C. None D. HA =; VA = = E. Inc. on ; dec.on F. Loc. min. f = G. CU on ; CDon Stewart: Calculus: Earl Transcendentals Seventh Edtion. ISBN: 58979. Cengage Learning. All rights reserved.. A. R B. -int.; -int. C. None D. None E. Inc. on dec.on F. Loc. ma. f = 7 G. CU on ; CDon. IP 6. A. R B. -int. -int. C. None D. None E. Dec. on R F. None G. CU on CDon. IP 7. A. { ±} B. -int. C. About -ais D. HA = VA = ± E. Inc. on ; dec.on F. Loc. min. f = G. CU on ;CDon 8. A. { 5} B. -int. C. None D. HA =VA 5 =5 E. Inc. on 5dec.on5 F. None G. CU on 5 5 =5

SECTION.5 SUMMARY OF CURVE SKETCHING 9. A. { } B. -int. -int. C. None D. HA = VA = E. Inc. on F. None G. CU on CDon. A. 5 5 B. -int. ±5 C. About the -ais D. None E. Inc. on 5 dec.on 5 F. None G. CD on 5 5 = =_. A. { } ± B. None C. About the origin D. HA =VA = = ± E. Inc. on ;dec.on F. Loc. min. f f = = loc. ma. G. CU on ;CDon. A. ] [ B. -int. are ± C. About the origin D. None E. Inc. on F. None G. CU on ;CDon. IP ± ± 9. A. { } B. -int. C. None D. VA = E. Inc. on ; dec.on F. Loc. min. f = G. CU on ;CDon. IP. A. [ B. None C. None D. HA = E. Dec. on F. None G. CU on _ 5. A. R B. -int. -int. C. None D. HA = ± E. Inc. on dec.on F. Loc. ma. f = G. CU on 7 + 7 ;CD on 7 + 7 +. IP 7 7+ 7 7 7 7 6 7 + 6 7 6. A. R B.-int. 7; -int. C. None D. None E. Inc. on 8 ; dec.on 8 F. Loc. ma. f 8 = loc.min.f = G. CD on Stewart: Calculus: Earl Transcendentals Seventh Edtion. ISBN: 58979. Cengage Learning. All rights reserved.

SECTION.5 SUMMARY OF CURVE SKETCHING 7. A. [ B.-int. C. None D. None E. Inc. on F. None G. CD on. A. R B. -int. C.About the-ais period D. None E. Inc. on n ndec.onn n + n an integer F. Loc. ma. f n =loc.min. f n + = n an integer G. CU on n + n + CDon n n +.IP n ± Stewart: Calculus: Earl Transcendentals Seventh Edtion. ISBN: 58979. Cengage Learning. All rights reserved. 8. A. B.-int. -int C.About -ais D. VA = ± E. Inc. on dec.on F. Loc. min. f = G. CU on =_ = 9. A. R B. -int. n + n an integer -int. C. Period D. None E. Inc. on n + n + 7 dec.on n n + n an integer F. Loc. ma. f n = loc.min.f n + = n an integer G. CU on n + n + 5 CDon n n + IP n + n an integer. A. B. None C. None D. VA = = E. Inc. on ;dec.on F. Loc. min. f =+ loc.ma.f = G. CU on CDon.IP. A. R Note: f is periodic with period soinb Gwe consider onl [ ] B. -int. 7 ; -int. C. Period D. None E. Inc. on 5 ;dec.on 5 F. Loc. ma. f = loc. min. f 5 = G. CU on 7 ;CDon 7.IP 7 ¹ _. A. R Note: f is periodic with period soinb Gwe consider onl [ ] B. -int. 5 ; -int. C. Period D. None E. Inc. on 6 7 ;dec. 6 on 6 7 6 F. Loc. ma. f 6 =loc.min. f 7 6 = G. CU on 5 ;CDon 5.IP 5 ¹ _6 ¹ 5¹ _ 7¹ 6

. A. R Note: f is periodic with period soinb Gwe consider onl [ ] B.-int. ; -int. C.Period D. None E. Inc. on ;dec.on F. Loc. ma. f = loc. min. f = G. CU on 6 5 ;CDon 5 6 6 6.IP 5 6 5 5 6 5. A. { } B. -int. e C. None D. HA = VA = E. Inc. on F. None G. CU on ;CDon.IP e SECTION.5 SUMMARY OF CURVE SKETCHING 5 G. CU on e / CDon e /.IP e / e / 9. A. B. -int. ± 5 C. None D. VA = = E. Inc. on dec.on F. None G. CD on. A.R B.-int -int C.About the -ais D. None E. Inc. on dec.on F. Loc. min. f = G. CU on ; CDon. IP± ln 6. A.R B.-int -int C.About the origin D.None E. Inc. on R F. None G. CU on CDon. IP. A. { n/} Note: f is periodic with period soin 7. A. { n <<n + n = ± ±...} Note: f is periodic with period so in B G we consider onl [ ] B.-int. ; -int. C.About the -ais period D. VA = E. Inc. on dec. on F. Loc. ma. f = f = G. CD on 8. A. B. -int. C. None D. HA =VA = E. Inc. on edec.one F. Loc. ma. f e =/e B-G we consider onl << B. -int. C. About the -ais period D. VA = = ± E. Inc. on dec.on F. None G. CD on ;CUon.IP ±. A. R B. -int -int C. None D. HA = E. Inc. on ; dec.on F. Loc. ma. f = e loc. min. f = G. CU on + ;CDon +. IP ± 6 ± e ± inflection points _ e@ -Ï +Ï Stewart: Calculus: Earl Transcendentals Seventh Edtion. ISBN: 58979. Cengage Learning. All rights reserved.

6 SECTION.5 SUMMARY OF CURVE SKETCHING. A. B.-int. C. None D. None E. Inc. on / e dec.on / e F. Loc. min. f / e = /e G. CU on e / CDon e /.IP e / / e 6. A. { } B. None C. None D. HA =VA = E. Inc. on ; dec.on F. Loc. min. f = e G. CU on e@ _. A. { } B. None C. None D. VA = E. Inc. on ; dec.on F. Loc. min. f = e G. CU on CDon 7. A. { } B. None C. None D. VA = E. Inc. on ; dec.on F. Loc. min. f = e G. CU on. Stewart: Calculus: Earl Transcendentals Seventh Edtion. ISBN: 58979. Cengage Learning. All rights reserved. 5. A.R B.-int -int. C.About the -ais D. HA = E. Inc. on ; dec.on F. Loc. ma. f ± = /e loc.min. f = G. CU on 5+ 7 5 7 5 7 CD on 5+ 7 5 7 5+ 7 ± 5 7. 5 7 5+ 7 ;.IPat = ± 5+ 7 _Œ º º Œ 8. A. B.-int. -int. C. None D. VA = E. Inc. on dec.on F. Loc. min. f = G. CU on =_