1. How is the natural logarithm function defined as an integral? What are its domain, range, and derivative? What arithmetic properties does it have? Comment on  its graph.

2. What integrals lead to logarithms? Give examples.

3. What are the integrals of tan x and cot x? sec x and csc x?

4. How is the exponential function e x defined? What are its domain, range, and derivative? What  laws of exponents does it obey? Comment on its graph.

5. How are the functions a x and log a x defined? Are there any restrictions on a? How is the graph of log a x related to the graph of ln x? What truth is there in the statement that there is really only one exponential function and one logarithmic function?

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PART 1  Why do we recreate the definition of Logarithmic function?

PART 2 Using FTC1 to define a new function.

PART 3 The Definition of Logarithms and Exponentials