MAT237Y1 Lecture : 3.1 tangent lines.pdf

• School: UTSG
• Department: Mathematics
• Course: MAT237Y1
• Professor: Dan Dolderman

Document Summary

3. 1 - tangent lines, velocity, and general rates of change. So, recall back when we rst started limits, i introduced to you the idea of a tangent line. Basically, you take a look at the secant lines, and take the limit as the second point approaches the rst. In other words, the slope of the tangent line is given by f(x) f(x0) x x0 lim x x0 where (x0, f(x0)) is the point at which we want to know the slope of the tangent line. Well, sometimes it"s a bit easier to take a limit to zero, than to have x x0. So, another way of thinking about this same tangent line is by rather than having x x0, we"re going to have the di erence between x and x0 go to zero. Then the slope of the tangent line is f(x0 + h) f(x0) h lim h 0.