This is an actual M403K midterm given on Thursday, September 26, 1991. On that test I allowed a ``crib sheet'' and a non-graphing calculator.
The syllabus has changed some in 9 years, so this exam doesn't cover exactly the same material as our first midterm will. In particular, problem 3 is Chapter 2 material, which will be tested in the second midterm.
Problem 1. Tangent lines
Consider the curve Find the equation of the line that is tangent to this curve at the point (1,-1).
Problem 2. Limits and continuity
Consider the function
a) Find , , and , if they exist.
b) Is f(x) continuous at x=2? Why or why not?
Problem 3. Graphs and optimization
Consider the function .
a) For what values of x is this function increasing? For what values of x is it decreasing?
b) On the interval [-1,3], find the maximum and minimum values of f(x) (and where these values occur).
Problem 4. Taking derivatives
Take the derivatives, with respect to x, of the following functions:
Problem 5. Taking limits
Evaluate the following limits: