Frontier High School

 • These mini-lessons are meant to show you "how to" complete certain problems in Calculus....Some of the "why" and extended discussion has been left for the classroom.....Use them as review or reinforcement for topics that you feel you need extra-help in....Most of these problems in these lessons coincide with your notes. Enjoy! 

 

Unit 1 - Limits  - A Graphical Approach  --->LimitsGraphically

                          - Algebraically  ---> LimAlgebraically

                          - Limits Approaching (+/-) Infinity  ---> LimsAppInfinity

                          - Horizontal and Vertical Asymptotes -----> Horiz/VertAsymptotes

                          - Continuity ------> DefinitionOfContinuity

                          - Trig Limits---> TrigLimits

                           - The Squeeze Theorem ---> The Squeeze (Sandwich)Theorem

 

 

Unit 2 - Derivatives ---> Slope of a Tangent Line/Equations of Lines -> SlopeofTangent

                                          - Higher Order Derivatives/Rule Check -> Higher Order Derivatives

                                          - Trig Derivatives ->  TrigDerivatives

Unit 3  - More with Derivatives....

            The Tan/Normal Line w/Horizontal & Vertical Tangents  ->       NormalHorizVert

            - Implicit Differentiation  -> ImpDiff

            - Trig Imp. Diff -> TrigImpDiff

            - Tan/Normal Lines with Imp Diff ->TanNormImpDiff

            - Higher Order Imp Diff -> HigherOrdImpDiff

 

Unit 3 cont.  - Linear Motion Characteristics -> LinMotExample1

            - Linear Motion Characteristics ->  LinMotExample2

 

Unit 4 - Graphing with Derivatives  -> GraphPOLYExample

                                                          -> GraphRATExample

                                                          -> GraphFRACEXPExample

                               Translate F' - F  ->  TranslateF'toF

 Unit 5- Optimization

                     - Example1 -> NumberProblem

                     - Example2 -> MoneyProblem

 

                    - Example 1 (BASIC)->RateExample1

                    - Example 2 (BASIC)-> RateExample2

                    - Example 3 (COMBO)-> RateExampl3

 

• Important Theorems 7a ----> Rolles/MeanValue

                                          ----->Intermediate Value Theorem

 

 

Unit 7b - Derivatives with e and ln ---> elnBasic Rules ->DiffRules of e/ln

                                                                 elnLine Examples -> eln with Lines

                                                                 eln Graphing (NonCalculator) ->Graphing #1

                                                                                       (Calculator) ->

Unit 8 - Derivatives with Inverses :  Inverse Trig Rules----->InverTrigExample

                                                          Derivative of an Inverse ---> DerivativeofInverseExample

 

Unit 9 - Integration:    Basic ---->  BasicIntegration

                                    Substitution--->IntegrateBYsubstitution

                                    Trig Integration---> TrigIntegration

                                 Reimann Sums (L/R/M) ---> LefRighMidpointExamples

                                  Note : Accidentally used the word "triangle" instead of rectangle...in 1st example...disregard...sorry.

                           Reimann Sums (Trap) ---> TrapExample

 

 Unit 10B - Definite Integral ---->  DefIntegralExamples

                   Area Under a Curve --> AreaUnderCurve

                   Area Between 2 Curves  --->  AreaBetweenTWOCurves

                   Area "BreakUps dx" ----> AreaBreakUpExamples

                   Area "right to Left dy" ---> AreaRighttoLeftExample

 

                  Using DisksWashers (x-axis) ----> DWXaxis

                  Using DisksWashers (y-axis) -----> DWYaxis

                  Using DisksWashers (x=a and y = b) -----> DWOther

                  Volume by Known Cross Sections---> VbyKnownCrossSec

                           Note: Last example with Semi Circles and Squares...interval from 0 to 2

 

               Average value Theorem -> AverageValueTheorem

               Rates with Accumulated Function --->RateswIntegration

               Motion Revisited ->PostionVelocityAccelerationwIntegration

               Distance/Displacement with Integration--> DistDispwInt

               Motion (Graphically)--> LinMotPt1 

                                                  LinMotPt2

                                                 LinMotPt3

                                                 LinMotPt4

 

 

                  LinMotSolutions

                  SquirrelsAnswers

 

Unit 13 -  Derivative of Definite Integral---> DerivativeofADefiniteIntegral

               Integration with e and ln  ---> Integrate 1/u ---> Integrate with Ln

                                                               Integrate e --> Integrate with e

               Diff EQ (Separation of Variables)--->SeparationOfVariables

               Diff Eq (Applications) --> InitialValueProblems

               Slope Fields--->   Slope Field #1 : SlopeField#1

                                            Slope Field #2(AP Question) :SlopeField#2