Midterm 3 14.01.10
Name:
Exercise 1. Compute the derivative of the following function:
f (x) = x x2+ 1. Solution:
1
Exercise 2. Compute the derivative of the following function:
f (x) = ex· log(x).
Solution:
2
Exercise 3. Compute the limit:
x→1lim
log(x) x − 1. Solution:
3
Exercise 4. Find the maximal and minimal values of the following function on the given interval:
f (x) = x2+ 2x + 21, [−2, 7].
Solution:
4
Exercise 5. Compute the integral:
Z
x2exdx.
Solution:
5
Exercise 6. Compute the integral:
Z x2 1 + x3. Solution:
6
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