MA140 Sample Exam #4
Date First name, Last name
Part I: 8 problems, 5 points each. Write answers in marked area.
Part II: 6 problems, 10 points each. Show all work for full credit.
Maximal score: 40 + 60 = 100 points.
Part I
1. Lisa Simpson is using Newton’s method to approximate a root of the function f(x) = x−cos x.
She starts with x0= 0. Find x2(three places after decimal point).
x2=
2. Find absolute maximum and minimum of the function g(x) = −cos x−sin x, where 0 ≤x≤π.
min:
max:
3. Find points of inflection of the function function h(x) = −x4+x2−1.
4. Find intervals, where function h(x) = −x4+x2−1 is increasing.
5. Evaluate the limit:
lim
x→0
1−cos x
x2+x
6. Evaluate the limit:
lim
x→0+x2ln x
1
