I Welcome You To The Class.  I Promise You That I Will Provide Thorough Coverage Of The Material.  You Will Feel At Ease After Watching This Video.  

You Will Know What It Means To Find The Limit Of A Function.  You Will Be Able To Discern Between Continuity At A Point Versus The Mere Existence Of A Limit At That Point.  You Will Learn What Assumptions Are Safe To Make In This Course.    

You Will Be Able To Distinguish Between Two Different Types Of Discontinuity.  An Empty Hole Situation Is Different From The Case Where Wild Oscillations Occur.  

You Will Be Able To Recognize And Understand One-Sided Limits.  

You Will Be Able To Recognize When A Function Is Continuous From One Side At A Point x=c But Not From The Other Side.  You Will Recognize The Fact That The Failure Of Continuity From One Side Of x=c Does Not Necessarily Mean The Non-Existence Of The Limit From That Side, Even Though The Non-Existence Of A Limit From One Side Of An Interior Point Will Imply That The Function Is Not Continuous From That Side.  For Endpoints, We Consider The Overall Limit To Be The One-Sided Limit That Honors The Domain Of The Function. For These Points, Continuity And One-Sided Continuity From The Honoring Side Are The Same. 

You Will Be Able To Recognize, Understand And Compute Horizontal Asymptotes.  You Will Have A Visual Understanding Of These Entities. 

You Will Be Able To Recognize And Understand Vertical Asymptotes.  You Will Have A Visual Understanding Of These Entities.

You Will Understand And Remember The Limit Rules.  You Will Need These Rules.

You Will Be Able To Apply The Limit Rules To A Wide Variety Of Problems.  The Students Will Recognize The Various Types Of Functions That Are Continuous At Any Point In Their Domain.

You Will Be Able To Identify Finite Valued Limits At Infinity As Horizontal Asymptotes Of The Given Function. You Will Be Able To Find These Horizontal Asymptotes By Doing Algebra And Then Plugging The Limit Value Into The 'Purified' Difference Quotient.  

You Will Be Able To Find Horizontal Asymptotes Of Rational Functions.  You Will Be Able To Do The Necessary Algebra When Solving These Problems.

You Will Recognize And Understand The Rule Concerning The Composition Of Continuous Functions.  You Will Recognize The Utility Of Having This Rule Available.  

You Will Be Able To Recognize Apply The Substitution Rule When It Is Needed.  The Student Will Be Able To Deal With Infinite Limits That Are Not Vertical Asymptotes.  The Student Will Understand What The Infinity Symbol Means.  

You Will Be Able To Define Euler's Constant.  You Will Be Able To Compute Exponential Variations In This Limit Definition Of Euler's Constant.  You Will Be Able To Compute Variations Of The Sinc Function.

You Will Be Able To Recognize And Apply The Intermediate Value Theorem When It Is Needed.  The Student Will Be Able To Recognize And Apply The Squeeze Theorem When It Is Needed.  

If The Limit Of A Function f(x) At A Point x=c Tends to Zero And If g Is Bounded On An Interval about x=c, Then The Limit Of The Product f(x)g(x) at x=c Will Equal Zero.  You Will Be Able To Recognize And Apply This Rule When It Is Necessary.

You Will Be Able To Apply Limits To The Heaviside And Step Functions.  You Will Recognize The Points Where Discontinuities Occur.  You Will Recognize Points Of Discontinuity Where Continuity From One Side Is Present/Absent.  

You Will Be Able To Find Limits That Involve The Conjugation Of Radicals.  You Will Be Able To Do Limits That Involve Variable Substitutions.  You Will Be Able To Solve Infinite Limits. 

You Will Be Able To Find Limits Whose Simplifications Involve Variations Of Factoring Via Difference Of Squares Or Difference Of Cubes.

You Will Be Able To Find The Limits At Infinity Of Differences Of Radicals.  You Will Be Able To Carry Out The Necessary Algebra In Order To Find This Limit.

You Will Understand The Derivative Concept.  You Will Be Able To Find The Derivative Of Simple Functions.

You Will Be Able To See The Relationship Between The Difference Quotient And The Derivative.  You Will See How The Tangent Line Slope Is The Derivative Of The Function At The Corresponding Point While The Secant Line Slope Is Equal To The Difference Quotient Of The Function Relative To The Corresponding Point And The 'Other' Chosen Point.

You Will Be Able To Find The Tangent Line To The Graph Of A Function At An Applicable Point.  You Will Recognize The Derivative Of The Function At This Point As The Slope Of The Aforementioned Tangent Line.

You Will Be Able To Find The Derivatives Of Quadratic Functions From First Principles.  

You Will Be Able To Find The Derivatives Of Some Basic Polynomial Functions From First Principles.  

You Will Be Able To Find The Derivative Of The Basic Absolute Value Function At Any Non-Zero Domain Point.  You Will Understand Why The Derivative Of The Absolute Value Function Does Not Exist At The Origin.

You Will Be Able To Find The Derivative Of The Square Root Function Along With Variations Of This Function.  You Will Know How To Find The Derivative Of The Most Basic Negative Power Functions.  

You Will Be Able To Find The Derivatives Of The Basic Positive And Negative Power Functions Along With The Cosine Function.  You Will Know How To Set Up The Process Of Finding The Derivative Of The Tangent Function.

You Will Be Able To Find The Derivative Of The Tangent Function and Cube Root Function From First Principles.  You Will Be Able To Find The Derivative Of Any Nth Root Function From First Principles.    

You Will Know How To Find The Derivative Of The Secant Functions From First Principles.  Assuming A Linear Numerator And A Linear Denominator, You Will Be Able To Find The Derivative Of Rational Functions From First Principles.  

You Will Know How To Extend The Definition Of Euler's Constant In Order To Evaluate Different Powers Of e.  You Will Know How To Find Infinite Limits Of Applicable Polynomials.  

You Will Be Able To Find Some Of The Vertical Asymptotes Of The Tangent Function And All Of The Horizontal Asymptotes Of The Inverse Tangent Function.  You Will Be Able To Evaluate Limits That Are Variations Of Familiar Limits Via Substitution.  You Will Be Able To Find The Horizontal Asymptote Of A Rational Function.

You Will Know How To Do The Derivative Of A Rational Function From First Principles.  

You Will Be Able To Differentiate Radical Functions Using First Principles.  You Will Know How To Set Up The Derivative Of The Cotangent Function.

You Will Be Fully Able To Find The Derivative Of The Cotangent Function From First Principles.

Sometimes A Function Will Be Continuous At A Point But Will Fail To Be Differentiable There.  This Can Be True Even If The Graph Of A Function Is 'Smooth' At A Point.  Indeed, We Can Get A Vertical Tangent At Such A Point. Sharp Points Are Also Examined.  You Will Be Able To Distinguish Between The Different Types Of Points At Which A Function Is Not Differentiable But Still Continuous.  

You Will Know How To Find The Tangent Lines At Applicable Points For The Graph Of A Given Function.  You Will Have A Greater Visual Appreciation Of The Derivative.

You Will Be Able To Apply The Shortcut Differentiation Rules To Concrete Problems.  These Rules Are Very Important And Convenient.  You Will Appreciate The Utility Of Not Having To Find Limits Each Time You Want The Derivative Of A Function.  

You Will Be Able To Do Any Differentiation Problem That Involves The Power Rule.  You Will Often Use The Power Rule In Calculus.

Students often find fractional exponents tricky.  Hence, I do examples that incorporate the power rule in the case of fractional exponents.

It is during this video that I introduce you to Chain Rule for the first time.  

I do more examples of the Chain Rule.  I really want you to learn the Chain Rule.