Section 7.8 Worksheet:

Assigned problems: Exercises pp. 397-399, #1, 2, 6, 10, 17, 18, 21, 50, 57, 83, 84

  1. Draw tex2html_wrap_inline235 and tex2html_wrap_inline237 on the intervals containing 0 for which they are one-to-one. Use the ``magic mirror'' (along the line y=x) to draw in the inverse functions ( tex2html_wrap_inline241 and tex2html_wrap_inline243 ).
  2. Graph the function tex2html_wrap_inline245 , and comment on the similarity to tex2html_wrap_inline243 . Both are called ``sigmoidal functions'', because they look like stretched and elongated ``S''es.

    table113

  3. The derivatives of the inverse trig functions open up new classes of functions that we can now integrate. For example, there was previously no way to analytically solve the integral

    displaymath233

    What would you write now?

Notes:

  1. There's risk of killing you with notation: be careful! By tex2html_wrap_inline241 here we mean arcsin(x), not tex2html_wrap_inline253 . Very bad of us!
  2. Inverse trig functions that I've known and loved: the two that I've used with any regularity are the arcsine and arctangent functions. Know those well: graphically, domains, ranges, derivatives, etc.


Wed Dec 12 10:29:55 EST 2007