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Calculus 2 - Final Exam Cheat Sheet (DRAFT) by

Calculus 2 Final Exam Sheet

This is a draft cheat sheet. It is a work in progress and is not finished yet.

II. Basic Techniques of Integr­ation

(i) Completing the Square
(ii) Polynomial Division
(iii) Separating Numerators

III. Basic Integr­ation Rules


IV. Integr­ation by Parts

(i) Choosing u dan dv (LIATE)
(ii) Repeated Iterations
(iii) Cycling

V. Trig Integrals

(i) Pythag­orean Identities
(ii) Half Angle and Double Angle Identities
(iii) Basic Trig Defini­tions
(iv) sin(u) cos(u) Integral Techniques
(v) sec(u) tan(u) Integral Techniques

I. Limits Review

(i) L'Hopitals Rule

VI. Trig Substi­tution

(i) Standard Substi­tutions
(ii) Reference Triangles
(iii) Converting Answers Back in Terms of x

VII. Partial Fractions

(i) Simple Roots
(ii) Repeated Roots
(iii) Factors without Roots
(iv) Solving for Unknown Constants (a) Setting Coeffi­cients Equal (b) Plugging in x-Values
(v) Integr­ation of Partial Fraction Decomp­osi­tions

VIII. Trapez­oidal Rule

(i) Error Estimate for Trapez­oidal Rule

IX. Simpson's Rule

(i) Error Estimate for Simpson's Rule

X. Improper Integrals

(i) Infinite Limits of Integr­ation
(ii) Integrands with Vertical Asymptotes

XIV. Series

(i) Conver­gence and Divergence
(ii) Sequence of Terms {an}
(iii) Sequence of Partial Sums {sn}
(iv) Harmonic Series
(v) Re-Ind­exing a Series
(vi) Absolute Conver­gence
(vii) Condit­ional Conver­gence

XV. Conver­gence Tests for Series

(i) Partial Sums
(ii) Nth Term Test/ Divergence Test
(iii) Geometric Series Test
(iv) Geometric Series Sum Formula
(v) P-Series Test
(vi) Integral Test
(vii) Remainder Theorem for the Integral Test
(viii) Direct Comparison Test
(ix) Limit Comparison Test
(x) Altern­ating Series Test
(xi) Remainder Estimation Theorem for the Altern­ating Series Test
(xii) Ratio Test
(xiii) Root Test

XIII. Sequences

(i) Conver­gence of a Sequence
(ii) Monotone Sequences
(iii) Bounded Sequences
(iv) Monotone Sequence Theorem/ Monotone Conver­gence Theorem

XII. Limit Comparison Test for Integrals


XI. Direct Comparison Test for Integrals


XVI. Power Series

(i) Interval of Conver­gence
(ii) Radius of Conver­gence
(iii) Ratio Test and Other Series Tests to Check Endpoints

XVII. Power Series Operations

(i) Compos­ition of a Power Series with a Continuous Function
(ii) Term by Term Differ­ent­iation
(iii) Term by Term Integr­ation

XVIII. Taylor and Maclaurin Series


XIX. Taylor Polyno­mials of Order n

(i) Approx­imating Function Values Using Taylor Polyno­mials
(ii) Degree vs. Order of a Taylor Polynomial

XX. Taylor's Theorem


XXI. Taylor's Formula


XXII. Remainder of Order n


XXIII. Remainder Estimation Theorem

(i) Finding an Upper Bound M for the Approp­riate Derivative of f(x)
(ii) Finding the Maximum Possible Error of a Taylor Polynomial Approx­imation
(iii) Finding the x-Values Where an Approx­imation will be within a Particular Error Tolerance

XXIV. List of Important Taylor Series to Memorize

(i) Developing new Taylor Series using substi­tution
(ii) Multip­lying Taylor Series by constants and powers of x

XXV. Parametric Equations

(i) Traveling Particle
(ii) Cartesian Equations vs. Parametric Equations and Converting
(iii) Domains for the Parameter
(iv) Parametric Equations for Lines
(v) Parametric Equations for Circles
(vi) the Natural Parame­ter­ization

XXVI. Arc Length of Curves


XXVII. Polar Coordi­nates

(i) Plotting Points in Polar Coordi­nates
(ii) Converting Between Rectan­gular and Polar Coordi­nates