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Topic: Calculus
Replies: 2   Last Post: Sep 21, 2004 11:27 AM

 Messages: [ Previous | Next ]
 Michael Livshits Posts: 212 Registered: 12/6/04
Re: Calculus
Posted: Jul 3, 2000 3:13 PM

On 3 Jul 2000, R. wrote:

> Find:
> lim (t+1)^9 * (t^2-1)
> x --> -2
> Would you just substitute in the -2 for the t's and figure it out
> algebraically?
>

Sure, you don't need limits to figure this one out, limits
should be used when you can't just plug in the numbers, for example,
sinx/x for x-->0 or (1+x)^x for x-->0. There are some artificially cooked
situations when you plug in and get the wrong number, for example,
f(x)=1 for x=/=0, f(0)=0, then lim (x-->0) f(x) = 1, while f(0)=0.
But if you deal with expressions involving the elementary functions,
you can plug in and get the limit. It's because the elementary functions
are continuous.

--Michael

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Date Subject Author
7/3/00 R.
7/3/00 Michael Livshits
9/21/04 Lisa Murphy