The Hyperbolic Tangent function.

1) Refer to the hyperbolic graph in the margin, and the text that accompanies it, on Page 261 of your text.
Use the exponential definitions of the Sinh and Cosh functions to find the exact coordinates of the point P when t = ln 8. For that value of t, how large is the corresponding shaded area in this graph?

2a) Let , the Hyperbolic Tangent function.
Given that , use Chain Rule to help find .
b) Use your calculator (or computing software) to help find the approximate values of when . (report each correct to four decimal places)

3a) Let , the inverse Hyperbolic Sine function.
Write down the “ln” form of this function, then use it to show what the exact value of g(x) is when x = -1.
b) Identify g’(x), then find the exact value of g’(x) when x = -1.

Sample Solution