Preview of Chapter 7
In this chapter we consider the topic of inverse functions, introduce 22 new functions and use l'Hopital's rule.  The 22 new functions consist of
2 logarithmic functions,
2 exponential functions,
6 inverse trigonometric functions,
6 hyperbolic functions and
6 inverse hyperbolic functions. (We actually don't cover these last 6 functions.)
For each one of these functions, mathematicians want to know about or how to do roughly a dozen things.

The "Dozen" Aspects of New Functions
1. define Define the function in terms of something already known.
2. evaluate Find values of the function used in expressions.
3. graph Draw graphs involving the function with and without technology.
4. properties Use the algebraic properties to simplify expressions.
5. proofs Prove or derive particularly informative results.
6. limits Take limits involving the function.
7. differentiate Use the chain rule and implicit differentiation with the function.
8. integrate Integrate indefinite and definite integrals.
9. tangent Find the equation of the tangent line to a curve involving the function.
10. area Find the exact area bounded by curves involving the function.
11. applications Solve related rates, max/min and other applications with the function.
As you are introduced to each of the 16 functions that we consider, analyze it against the list above.