MAT 294
The Mathematics of Change I
Fall 2005
Exam 1
Be able to find limits of a function at a point using
direct substitution
factor and cancel
simplify complex or multiple fractions (then factor and cancel)
rationalize the numerator or denominator (then factor and cancel)
Be able to find the limit of a function at infinity (horizontal asymptotes)
analyzing general trends
dividing all terms by the highest power of x
Know the terminology and notation from
the approximation framework
the functions framework
the rate of change framework
Be able to answer any of the five approximation questions in any representation for
the Mystery Constant problems (see the group write-ups and comments)
the Rate of Change problems (see the group write-ups and comments)
The problems from written assignment #3 or similar
Be able to find derivatives
using the limit definition and basic techniques for evaluating limits (see above)
Be able to use derivative information to
find the slope of a tangent line
find the instantaneous rate of change of a process at some point
equation of a tangent line (linear model)
Be able to explain why the limit definition of the derivative is what it is in terms of the approximation framework
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