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Contents
1. Limit of the sequence 3
1.1. LimitLawsforConvergentSequences......... 5
2. Limit of a Function 8
2.1. Calculating Limits Using the Limit Laws . . . . . . . 9
2.2. LimitLaws ....................... 9
3. Continuity 11
4. Derivatives 15
4.1. Velocities ........................ 15
4.2. Definition of the Derivative . . ............ 16
4.3. Tangents......................... 17
4.4. Othernotations..................... 17
4.5. OtherRatesofChange................. 19
4.6. Derivativesofelementaryfunctions .......... 20
4.7. TheChainRule..................... 21
4.8. Implicit Differentiation . ................ 21
4.9. DifferentiationoftheInverseFunction ........ 24
4.10.ParametricCurves ................... 26
4.11.TangentstoParametricCurves ............ 28
4.12.HyperbolicFunctions.................. 29
4.13.TheSecondDerivative ................. 30
5. More Applications of the Derivative 30
5.1. Certain Theorems About Differentiable Functions . . 30
5.2. Limits Involving Infinity ................ 31
5.3. Indeterminate Forms and L’Hospital’s Rule . . . . . . 31
6. Linear Approximations 35
Bibliography 36
37
