1. What are the six basic hyperbolic functions? Comment on their domains, ranges, and graphs. What are some of the identities relating them?

2. What are the derivatives of the six basic hyperbolic functions? What are the corresponding integral formulas? What similarities do you see here with the six basic trigonometric functions?

3. How are the inverse hyperbolic functions defined? Comment on their domains, ranges, and graphs. How can you find values of  using a calculator’s keys for

?

4. What integrals lead naturally to inverse hyperbolic functions?

Part 1: Hyperbolic function 

1. Definition of hyperbolic function 

2. Identities 

3. Introduction of Application

Note: In the graph of hyperbolic cosine, two functions are mislabeled.  The correct graph is shown below.

Part 2: The derivative and Integral of Hyperbolic function 

1. The derivative of sinhx,coshx,tanhx 

2. Formulas

Part 3: Examples 

Note: The method in the video above cannot calculate the integral of cot(x), the correct way to find the integral is 

 .

Part 4:Inverse Hyperbolic Functions

1. Why does hyperbolic sine have inverse function?
   

2. The derivative of inverse hyperbolic sine.

3. Useful indentities

4. Formulas

Note: In handwritten notes,replace the word "y" to "x" as shown below.