(Section 1.5: PiecewiseDefined Functions; Limits and Continuity in Calculus)
1.5.8
PART F: LIMITS IN CALCULUS
Example 7 (Limits and the Greatest Integer or Floor Function)
Let
fx
()
=
x
±
²³
´
µ¶
or
x
±
²
³
´
.
A LeftHand, OneSided Limit
Evaluate
lim
x
±
2
²
, which is read:
“the limit of
as
x
approaches
2 from the left
.”
• We want the real number that
approaches as
x
approaches 2
from
lesser
numbers (imagine approaching
x
=
2
from the
left
along
the real number line), if such a number exists.
• A table can help:
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 Spring '09
 Continuity, Limits, real number line

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