It is expected that students will:

• model and apply inverse trigonometric, base e exponential, natural logarithmic, elementary implicit, and composite functions to solve problems

Find the area of the part of the first quadrant that is inside the circle and to the left of the line x = u. (The inverse sine function will be useful here.)

Suppose that under continuous compounding 1 dollar grows after t years to dollars. Find the number r such that . (This r is called the nominal yearly interest rate.)

• draw (using technology), sketch and analyse the graphs for rational, inverse trigonometric, base e exponential, natural lograithmic, elementary implicit and composite functions, for:
  - domain and range
  - intercepts

Sketch the graph of .

Write in a form that does not involve any trigonometric functions.

a) Let f(x) - ln(ex). Sketch the graph of f(x).
b) Let g(x) be the inverse function of f(x). Sketch the graph of g(x).
c) Find an explicit formula for g(x).

Sketch the curve .

• recognize the relationship between a base a exponential function (a>0) and the equivalent base e exponential function
  

Let .
a) Express f(x) in the form .
b) Find the minimum value taken on by f(x) on the interval
.

• determine using the appropriate method (analylitic or graphing utility) the points where f(x) = 0

[No example for this prescribed learning outcome]