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Topic: Is (t^2-9)/(t-3) defined at t=3?
Replies: 166   Last Post: Oct 30, 2013 9:41 AM

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Richard Tobin

Posts: 1,267
Registered: 12/6/04
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Sep 29, 2013 8:29 AM
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In article <5c-dnS8w3YRi4trPnZ2dnUVZ_o-dnZ2d@megapath.net>,
Hetware <hattons@speakyeasy.net> wrote:

>(x+y)(x-y)/(x-y) not defined for x=y appears to be a pedagogical device
>which I am not convinced will stand closer scrutiny.


No.

>The essence of the
>lesson is that a function can have a limit as its argument approaches a
>value for which the function is not defined.


Yes, and it can also have a limit at some value where the function *is*
defined, but the value of the limit is not the value of the function.

For example, this is a perfectly good function:

f(x) = x+3 (x != 3)
f(3) = 42

-- Richard


Date Subject Author
9/28/13
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Hetware
9/28/13
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Michael F. Stemper
9/28/13
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scattered
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Hetware
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quasi
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Hetware
9/28/13
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quasi
9/28/13
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Peter Percival
9/29/13
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quasi
9/28/13
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Hetware
9/28/13
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Richard Tobin
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Hetware
9/28/13
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tommyrjensen@gmail.com
9/29/13
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Hetware
10/6/13
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Hetware
10/6/13
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Peter Percival
10/6/13
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Hetware
10/6/13
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quasi
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quasi
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Michael F. Stemper
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Hetware
9/29/13
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quasi
9/29/13
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Hetware
9/29/13
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magidin@math.berkeley.edu
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Hetware
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magidin@math.berkeley.edu
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Hetware
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LudovicoVan
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Peter Percival
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10/12/13
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Hetware
10/12/13
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fom
10/13/13
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Richard Tobin
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Hetware
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Peter Percival
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fom
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fom
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10/13/13
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10/14/13
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10/16/13
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10/19/13
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Hetware
10/19/13
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10/19/13
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Hetware
10/20/13
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quasi
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Hetware
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fom
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Hetware
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Peter Percival
10/20/13
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Richard Tobin
10/20/13
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Hetware
10/30/13
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10/19/13
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Hetware
10/10/13
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Ronald Benedik
10/10/13
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Peter Percival
10/10/13
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Virgil
10/18/13
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Hetware
10/19/13
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Peter Percival
10/19/13
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fom
10/19/13
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Peter Percival
10/19/13
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Hetware
10/19/13
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Peter Percival
10/19/13
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Hetware
10/19/13
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fom
10/19/13
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magidin@math.berkeley.edu
10/19/13
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Hetware
10/19/13
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magidin@math.berkeley.edu
10/20/13
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Hetware
10/20/13
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quasi
10/20/13
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Hetware
10/20/13
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Peter Percival
10/20/13
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magidin@math.berkeley.edu
10/20/13
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Hetware
10/20/13
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Arturo Magidin
10/20/13
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Hetware
10/20/13
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10/19/13
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