


Words From HongJian:


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. 








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·
Determine the domain of a function ·
Evaluate a function ·
Evaluate composition functions 


·
Determine the equation of a straight line in the plane 


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


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


·
Compute the derivative by definition: The four step procedure ·
Find an equation of the tangent line (using the 4step procedure to
find slopes) 


·
Compute limits: using the basic trigonometric limit 


·
Compute limits: using the Squeeze Law 


·
Compute side limits (infinite limits) 


·
Check continuity of functions and determine discontinuities 


·
Application of the intermediate value property of continuous
functions 


·
Find derivatives by using differentiation rules 


·
Find derivatives by using the chain rule 


·
Find vertical tangent lines 


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


·
Compute derivatives of trigonometric functions 


·
Compute derivatives of implicit functions 


·
Compute related rates 


·
Compute the differential and linear approximation of a function 


·
Determine monotone intervals of a function 


·
The Mean Value Theorem 


·
The First Derivative Test and the classification of critical points
(open interval minmax problems) 


·
Compute the higher derivatives 


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


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


·
Differentiation and Antidifferetiation 


·
Compute antiderivatives with some algebraic skills and substitution
techniques 


·
Substitution? Which one? 


·
Compute Sums with summation notation 


·
Riemann Sums and definite integrals 


·
Evaluation of integrals 


·
Average of a function 


·
Fundamental Theorem of Calculus 


·
Volume Computing 


·
Arc length and surface area computing 








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