Name:
MATH 19900—00
Review for Exam #1
1. Theory:
(a) State and interpret both parts of the Fundamental Theorem of Calculus.
(b) What does it mean to be an antiderivative of a function f?
(c) Does every function have an antiderivative? Does every continuo

MATH 19900-00
Basic Antiderivatives
Fill in the following table, where F (x) is a particular antiderivative of f (x).
given function, f (x)
k, where k is a constant
xn for n 6= 1
1
,
x
x>0
sin x
cos x
sec x tan x
sec2 x
ex
1
1+x2
1
1x2
kf (x), where k is

Distance and Area
1. Suppose that a person is taking a walk, and walks at a constant rate of 3 miles per hour along
a long straight path.
(a) Sketch a labeled graph of the function v(t) = 3. Be sure to label your axes with the
appropriate units.
(b) How f

Name:
MATH 19900-00
Review for Final Exam
For the final exam, you can expect at least 80% of the questions to be based on material since
the last exam (average value, applications to physics, differential equations, and sequences), and
the rest to be over

Name:
MATH 19900-00
Review for Exam #2 - Answers
1. Theory:
(a) State both parts of the Fundamental Theorem of Calculus.
Z b
f (x) dx is an improper integral?
(b) How do you know if
a
(c) What is the form of the partial fraction decomposition for a ration