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(Section 2.1: An Introduction to Limits)
2.1.21.
FOOTNOTES
1.
Limits do not require continuity.
In a later section, we will discuss continuity, a property of
many functions that helps the lovers run along the graph of a function without having to jump
or hop. In the first few problems of this section, we had the luxury of imagining the lovers
running towards each other (one from the left, one from the right) while staying on the graph
of
f
and without having to jump or hop, provided they were placed on appropriate parts of
the graph. Sometimes, the “run” really requires jumping or hopping.
For example, consider
the following function
f
. It turns out to be true that
lim
x
±
0
fx
()
=
0 .
=
0,
if
x
is a rational value
x
,i
f
x
is an irrational value
±
²
³
2.
Misconceptions about limits.
See “Why Is the Limit Concept So Difficult for Students?” by Sally Jacobs in the Fall 2002
edition (vol.24, No.1) of
The AMATYC Review
, pp.2534.
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.
 Fall '10
 sturst
 Continuity, Limits

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