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Practice ProblemsPaul Dawkins
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Chapter 1 / Exercise 3
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
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Calculus II – Practice Problemsi© 2018 Paul DawkinsTable of ContentsPreface.................................................................................................................................................................iiiOutline..................................................................................................................................................................ivChapter 1 : Integration Techniques........................................................................................................................1Section 1-1 : Integration by Parts..............................................................................................................................3Section 1-2 : Integrals Involving Trig Functions.........................................................................................................4Section 1-3 : Trig Substitutions..................................................................................................................................5Section 1-4 : Partial Fractions....................................................................................................................................7Section 1-5 : Integrals Involving Roots......................................................................................................................8Section 1-6 : Integrals Involving Quadratics..............................................................................................................9Section 1-7 : Integration Strategy...........................................................................................................................10Section 1-8 : Improper Integrals..............................................................................................................................11Section 1-9 : Comparison Test for Improper Integrals............................................................................................12Section 1-10 : Approximating Definite Integrals.....................................................................................................13Chapter 2 : Applications of Integrals....................................................................................................................14Section 2-1 : Arc Length..........................................................................................................................................15Section 2-2 : Surface Area.......................................................................................................................................16Section 2-3 : Center of Mass...................................................................................................................................17Section 2-4 : Hydrostatic Pressure and Force.........................................................................................................18Section 2-5 : Probability..........................................................................................................................................20Chapter 3 : Parametric Equations and Polar Coordinates.....................................................................................21Section 3-1 : Parametric Equations and Curves......................................................................................................23Section 3-2 : Tangents with Parametric Equations.................................................................................................25Section 3-3 : Area with Parametric Equations.........................................................................................................26Section 3-4 : Arc Length with Parametric Equations...............................................................................................27Section 3-5 : Surface Area with Parametric Equations............................................................................................28Section 3-6 : Polar Coordinates...............................................................................................................................29Section 3-7 : Tangents with Polar Coordinates.......................................................................................................31Section 3-8 : Area with Polar Coordinates..............................................................................................................32Section 3-9 : Arc Length with Polar Coordinates.....................................................................................................33Section 3-10 : Surface Area with Polar Coordinates...............................................................................................34Section 3-11 : Arc Length and Surface Area Revisited............................................................................................35Chapter 4 : Series & Sequences............................................................................................................................36Section 4-1 : Sequences..........................................................................................................................................39Section 4-2 : More on Sequences............................................................................................................................40Section 4-3 : Series - The Basics..............................................................................................................................41Section 4-4 : Convergence/Divergence of Series....................................................................................................42Section 4-5 : Special Series......................................................................................................................................43Section 4-6 : Integral Test........................................................................................................................................44Section 4-7 : Comparison Test/Limit Comparison Test...........................................................................................45Section 4-8 : Alternating Series Test.......................................................................................................................46Section 4-9 : Absolute Convergence.......................................................................................................................47Section 4-10 : Ratio Test..........................................................................................................................................48Section 4-11 : Root Test..........................................................................................................................................49Section 4-12 : Strategy for Series............................................................................................................................50
Calculus II – Practice Problemsii© 2018 Paul DawkinsSection 4-13 : Estimating the Value of a Series.......................................................................................................51Section 4-14 : Power Series.....................................................................................................................................52Section 4-15 : Power Series and Functions.............................................................................................................53Section 4-16 : Taylor Series.....................................................................................................................................54Section 4-17 : Applications of Series.......................................................................................................................55Section 4-18 : Binomial Series.................................................................................................................................56Chapter 5 : Vectors..............................................................................................................................................57Section 5-1 : Vectors - The Basics............................................................................................................................58Section 5-2 : Vector Arithmetic...............................................................................................................................59Section 5-3 : Dot Product........................................................................................................................................60Section 5-4 : Cross Product.....................................................................................................................................61Chapter 6 : 3-Dimensional Space.........................................................................................................................62Section 6-1 : The 3-D Coordinate System................................................................................................................64Section 6-2 : Equations of Lines..............................................................................................................................65Section 6-3 : Equations of Planes............................................................................................................................66Section 6-4 : Quadric Surfaces................................................................................................................................67Section 6-5 : Functions of Several Variables...........................................................................................................68Section 6-6 : Vector Functions................................................................................................................................69Section 6-7 : Calculus with Vector Functions..........................................................................................................70Section 6-8 : Tangent, Normal and Binormal Vectors.............................................................................................71Section 6-9 : Arc Length with Vector Functions......................................................................................................72Section 6-10 : Curvature..........................................................................................................................................73Section 6-11 : Velocity and Acceleration.................................................................................................................74Section 6-12 : Cylindrical Coordinates.....................................................................................................................75Section 6-13 : Spherical Coordinates......................................................................................................................76
Calculus II – Practice Problemsiii© 2018 Paul DawkinsPrefaceHere are a set of practice problems for the Calculus II notes.If you are viewing the pdf version

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Term
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RUBIN
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Polar coordinate system
We have textbook solutions for you!
The document you are viewing contains questions related to this textbook.
The document you are viewing contains questions related to this textbook.
Chapter 1 / Exercise 3
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Tan
Expert Verified