Millersville University Name
Mathematics Department
MATH 161, Quiz 2
January 23, 2004
Please answer the following questions. Your answers will be evaluated on their correctness,
completeness, and use of mathematical concepts we have covered. Please show all work and
write out your work neatly. Answers without supporting work will receive no credit.
1. Find and identify (removeable, jump, or infinite) the discontinuity of the function
f(x) = x2−1
x−1.
Explain your answer fully.
Since f(x) is undefined at x= 1, it must have a discontinuity at x= 1.
We can see that the
lim
x→1
x2−1
x−1= lim
x→1
(x−1)(x+ 1)
x−1
= lim
x→1(x+ 1)
= 2.
Since the two-sided limit exists as x→1, f(x) has a removeable discontinuity at x= 1.
