Challenge Problems for SSEA 41, Homework 1
Read Stewart’s Appendix D on the /δ definition of a limit, and then try the following
questions.
(1) Using the /δ definition of a limit, show that
lim (2x − 5) = 1.
x→3
This type of problem has been known to show up on Math 41 midterms.
(2) Using the /δ definition of a limit, show that
√
lim x = 0.
x→0
(3) Using the /δ definition of a limit, prove the limit law that states that if c is a real
number and if limx→a f (x) exists, then
lim cf (x) = c lim f (x).
x→a
x→a
(4) Using the /δ definition of a limit, prove the limit law that states that if limx→a f (x)
and limx→a g(x) exist, then
lim f (x) + g(x) = lim f (x) + lim g(x).
x→a
x→a
x→a
(5) Explain how to do the magic trick with a die demonstrated in class. How does the
magician know whether the volunteer performed the last 90◦ rotation or not?
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