MATH127 Lecture 4: Note Week 4.pdf
6 Aug 2014
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You should read section 2. 1 of the textbook and do exercise 2, 5. The tangent line to a curve is a line that touches the curve having the same direction as the curve at the point of contact. Finding the slope of the tangent line will tell us the slope of the curve. We know how to nd the slope of a line given two points so we will construct a line segment called the secant line that touches the curve at two points. As we move the second point closer to the rst point, the secant line becomes closer to the tangent line. Certainly, we can calculate an average velocity as the change in position over the time elapsed. If we make the time elapsed interval very small, we get closer to the instantaneous velocity. Both the tangent and instantaneous velocity problem involve the notion of a limit.
