Supplemental Notes: review topics
Examples of Simplication that we would see in calculus.
Basic information on exponential functions and logs
Examples on solving logs.
Limits are y-values . . . Some function are put together nicely, where if two x-values are close to each other then the associated y-values will also be close to each other. However, some times you'll have functions that have "problem" areas (ie: vertical assymptotes, holes, breaks). One way to think about limits is that they give the y-value of your function at the given x in utopia.
A list of the limit rules as well as special cases.
A worked example of an instantaneous velocity question (hint: it's really a limit question).
The formal definition of a limit with an example.
Worked examples on computing the limits as x approaches infinity.
The intermediate value theorem and some examples.
lecture notes on the formal definition of a limit.
A list of all the derivative rules.
The reasons why the derivative rules work.
Finding the derivative at a point using the limit definition of the derivative (similar to webwork section 2.1, question 1)
Finding the derivative of complicated functions
(solutions key)
2 worked examples on implicit differentiation
Strategies for solving a related rates question.
A sample related rates question (the distance between 2 cars).
More worked examples of related rates questions.
The basics of linearization: linear approximation
The main application of linear approximation: estimating roots
The basics of differentials
Proof and example using the formula for the derivative of the inverse of a function.
Why L'Hospital's rule works (for the 0/0 case).
Summary of Calculus I Topics
Chart of Common Derivatives and anti-derivatives.
A checklist for the steps for sketching a curve and an example -- worked out.
A checklist for the steps for optimization questions and 2 examples -- worked out.
More worked examples for optimization situations.
The basics of Newton's Method.
The Newton's method handout and
solutions
A use for Newton's Method: continuous fractions
A few examples dealing with antiderivatives.