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  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