Properties of Limits
Read this section to learn about the properties of limits. Work through practice problems 1-6.
Tangent Lines as Limits
If we have two points on the graph of a function, and , then and so the slope of the secant line through those points is and the slope of the line tangent to the graph of at the point is, by definition,
Example 3: Give a geometric interpretation for the following limits and estimate their values for the function in Fig. 5:
Solution: Part (a) represents the slope of the line tangent to the graph of at the point so
. Part (b) represents the slope of the line tangent to the graph of at the point so .
Practice 4: Give a geometric interpretation for the following limits and estimate their values for the function in Fig. 6: