MATH-1200 Lecture 14: MATH 1200-LECTURE 14- Limits

• School: Vanderbilt University
• Department: Mathematics
• Course: MATH-1200
• Professor: Pamela Pigg

Document Summary

L f(b) f(a) y= f(x: slope(m) of a secant line is the average rate of change or average velocity, shown by the line l in figure 1. m = f(b ) A a: x b x, slope(m) of a tangent line represents the instantaneous rate of change or instantaneous velocity. Figure 1: tangent line will occur as x approaches to 0. Example: given the function and the time intervals, find the average rate of change and the instantaneous rate of change. y = x. As x approaches to 0, m will approach to 2 which is the slope for the tangent line and the instantaneous rate of change. The limit of f(x) equals to l as x approaches a x is approaching to a but not equals to a. Function f (x) = l only exist if and l1 = l2 lim x a f (x) = l1 lim x a lim x a+ f (x) = l2.