next up previous
Next: About this document Up: The linear approximation Previous: Background

Exercises

  1. Try out tangentline on the following examples. This part of the lab is intended to help you become more familiar with the concept of the tangent line to a function at a point x=a. Use the given values of a along with another value of your choice.
    1. with a = 2 and a = -3.
    2. with a = 0 and .
    3. with a = 2 and a = -1.

  2. More generally, the graphs of two functions and are tangent at x=a if and . For example, the functions and are tangent at x=0, but the functions and are not tangent at x=0, even though they have the same slope, because and so the graphs of p and q don't intersect at x=0.

    Show that is tangent to at x=a under this more general definition.

  3. Suppose that and . Determine if the following statements are true or not.
    1. is tangent to at x=-1.
    2. is tangent to at x=1.
    3. is tangent to at x=1.



Sean O Anderson
Wed Sep 20 11:01:11 EDT 1995