Example midterm 1

Example midterm 2

Way too short solutions to example midterm 2

Below are links to some sample finals (the ones of Kouba are actually three 'midterms' which together test all the material).

Gravner

Kouba 1

Kouba 2

Kouba 3

Vershynin 1

Vershynin 2

A useful resource is Kouba's website with full solutions to several exercises from the book.

The final (tentatively) will have seven questions for a total of 100 points.

- In Exercise 1 you have to compute 8 limits (3 points each).
- In Exercise 2 you have to compute the first derivatives of 4 functions (3 points each).
- In Exercise 3 you have to compute the absolute maximum and absolute minimum of 4 functions or indicate why these do not exist (4 points each).
- In Exercise 4 you have to determine, using first and second derivatives, where a certain function is increasing/decreasing and concave up/concave down and you have to determine local maxima and minima (total of 18 points).
- Exercise 5, 6 and 7 (10 points each) are theory exercises. They will deal with: the intermediate value theorem, the extreme value theorem, the mean value theorem and increasing functions. You will have to use the definitions of limit and derivative at certain (but not all) points.