Lecture 10
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Assignment
2.1 Tangents 1, 3-5 2/6
2.2 Limits 1-4, 7, 9, 15 2/6
2.3 Calculating Limits 1-8, 29, 31-32 2/6
We spent the lecture finding from scratch the slope of the
line tangent
to the graph of the function y=x² at the point (1,1).
We discussed the need to look at both sides of the graph; ie,
cover up the part of the graph to the right of x=1 including
x=1 itself to find the limit from the left of
the difference quotient. Then to the same for the right side.
Notice that both times we `predict' that the value of
the function (f(x)-f(1))/(x-1) has the value 2, even though
the function is not defined at x=1.