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==<span style="font-size:20px; color: blue;">Limits</span>== | ==<span style="font-size:20px; color: blue;">Limits</span>== | ||
This section covers limits and some other precalculus topics. | This section covers limits and some other precalculus topics. | ||
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[[User:Temperal/The Problem Solver's Resource6|Back to page 6]] | [[User:Temperal/The Problem Solver's Resource8|Continue to page 8]] | [[User:Temperal/The Problem Solver's Resource6|Back to page 6]] | [[User:Temperal/The Problem Solver's Resource8|Continue to page 8]] | ||
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Latest revision as of 19:19, 10 January 2009
Introduction | Other Tips and Tricks | Methods of Proof | You are currently viewing page 7. |
Limits
This section covers limits and some other precalculus topics.
Definition
is the value that
approaches as
approaches
.
is the value that
approaches as
approaches
from values of
less than
.
is the value that
approaches as
approaches
from values of
more than
.
- If
, then
is said to be continuous in
.
Properties
Let and
be real functions. Then:
Squeeze Play Theorem (or Sandwich Theorem)
Suppose is between
and
for all
in the neighborhood of
. If
and
approach some common limit L as
approaches
, then
.
Diverging-Converging Theorem
A series converges iff
.
Focus Theorem
The statement is equivalent to: given a positive number
, there is a positive number
such that
.