Summary: Math 1550 Fall 2005
Section 31 P. Achar
Exam 1 Solutions
September 15, 2005
Total points: 50 Time limit: 1 hour
No calculators, books, notes, or other aids are permitted. You must show your work and justify your
steps to receive full credit.
1. (5 points) Short Answer:
(a) Complete the following sentence with the definition of continuity: We say that f(x) is continuous
at x = a if . . .
Solution: . . . lim
f(x) = f(a). OR: . . . f(a) is defined, lim
f(x) exists, and the two are equal.
(b) Explain why the following reasoning is incorrect:
Let f(x) = [[x]]. We know that f(1.5) = 1 and f(2.5) = 2. Also, 1.3 is between 1 and
2, so according to the Intermediate Value Theorem, there must be a point c between 1.5
and 2.5 where f(c) = 1.3.
Solution: The Intermediate Value Theorem only applies to continuous functions. The greatest