Hong-Jian's Tips on Calculus

 

 

 

Words From Hong-Jian:

 

This is the area where you may find something arisen from working on the problems in Calculus. Now it is in the beginning stage. I hope this will grow and will offer Calculus learning students certain help outside the classroom. Students are the most important for making this place to grow and to become a spot where the Calculus learning students would find helpful. Please send your feedback and suggestions to me at hjlai@math.wvu.edu and I will appreciate your comments very much.

 

 

 

 

 

 

 

 

 

Click the Tip to see if that will be helpful for you. All these reviews are in PDF format, which may require an Acrobat Reader to view them. If you do not have an Acrobat Reader, you can download one free by clicking Acrobat Reader.

 

 

 

 

 

 

 

 

 

 

 

 

 

Tip

        Determine the domain of a function

        Evaluate a function

        Evaluate composition functions

 

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        Determine the equation of a straight line in the plane

 

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        Calculate the limit of a function: Apply Limit Laws and Properties

 

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        Calculate the limit of a function: canceling zero factors before evaluating for the 0/0 type limits, and other hard to decide situations

 

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        Compute the derivative by definition: The four step procedure

        Find an equation of the tangent line (using the 4-step procedure to find slopes)

 

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        Compute limits: using the basic trigonometric limit

 

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        Compute limits: using the Squeeze Law

 

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        Compute side limits (infinite limits)

 

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        Check continuity of functions and determine discontinuities

 

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        Application of the intermediate value property of continuous functions

 

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        Find derivatives by using differentiation rules

 

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        Find derivatives by using the chain rule

 

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        Find vertical tangent lines

 

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        Find maximum and minimum values of a function over a closed interval

 

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        Compute derivatives of trigonometric functions

 

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        Compute derivatives of implicit functions

 

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        Compute related rates

 

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        Compute the differential and linear approximation of a function

 

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        Determine monotone intervals of a function

 

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        The Mean Value Theorem

 

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        The First Derivative Test and the classification of critical points (open interval min-max problems)

 

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        Compute the higher derivatives

 

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        Applications of the second derivative: the concavity of the graph and the second derivative test

 

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        Study the behavior of a function at infinity and asymptotes of the graph of a function

 

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        Differentiation and Antidifferetiation

 

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        Compute antiderivatives with some algebraic skills and substitution techniques

 

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        Substitution? Which one?

 

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        Compute Sums with summation notation

 

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        Riemann Sums and definite integrals

 

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        Evaluation of integrals

 

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        Average of a function

 

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        Fundamental Theorem of Calculus

 

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        Volume Computing

 

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        Arc length and surface area computing

 

 

 

 

 

 

 

 

 

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