Limit Rules and Derivative Rules
Willard Miller
September 12, 2005
0. 1 Limit Rules
We will make use of the following limit rules in this course, without any
rigorous proof. For most of the functions we encounter, these rules should
seem intuitively obvio

The Mean Value Theorem and the Extended
Mean Value Theorem
Willard Miller
September 21, 2006
0.1 The MVT
Recall the Extreme Value Theorem (EVT) from class: If the function f is
dened and continuous on a closed bounded interval [a, b] then there is some
po

Math 1271 Final Exam Spring 2005
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Math 1271 Final Exam Fall 2005
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and Institute of Technology policies on Scholastic Conduct. S

0.1 Newtons method and the Mean Value
Theorem
Newtons method for computing the zeros of functions is a good example of
the practical application of the Mean Value Theorem. Let f (as) be a real-
valued function on the real line that has two continuous deri