AP微积分章节练习

Chapter2LimitsandContinuity

Exercise1

Evaluateeachofthefollowinglimits.

2.

3.

4.

5.

6.

7.

Chapter4Differentiating

&

Chapter5Advancedtopicsindifferentiation

19.

20.Computingthederivativeofthefollowingfunctions.

Findthefirsttwoderivativesofeachofthefollowingfunctions

Chapter6Applicationsofthederivatives

Chapter7Integration

&

Chapter9Applicationsofintegration

Evaluatingtheindefiniteintegralofthefollowingfunctions.

Chapter10DifferentialEquations

1.Ifthedifferentialequationisgivenas

,

rewriteitintheform

,

where

2.

Findtheintegratingfactor

.

3.

Evaluatetheintegral

4.

Writedownthegeneralsolution

.

5.

IfyouaregivenanIVP,usetheinitialconditiontofindtheconstantC.

6.Considertheautonomousequation

withparametera.

(1).Drawthebifurcationdiagramforthisdifferentialequation.

(2).Findthebifurcationvaluesanddescribehowthebehaviorofthesolutionschangesclosetoeachbifurcationvalue.

7.Solvetheequation

knowingthaty1=2isaparticularsolution.

8.Findallthesolutionsof

9.Findallthesolutionsto

10.Considertheautonomousdifferentialequationwiththeinitialcondition.

(1).Find.

(2).FindthefirstfivetermsoftheEulerApproximationwhen.

(3).Isthereacontradictionbetweentheresultsof1and2?Ifyes,explainwhathappened.

11.Findtheapproximatedsequence,fortheIVP

.

12.Findthesolutionof

13.LetbethesolutiontotheIVP

andbethesolutiontotheIVP

FindtheWronskianof.Deducethegeneralsolutionto

14.FindthegeneralsolutiontotheLegendreequation

,

usingthefactthatisasolution.

15.Findthesolutiontothe