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Old 10-16-2001, 03:01 AM   #1
optimistic
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Join Date: Apr 2001
Posts: 3,006
Default HW help in calc

Show by means of an example that lim x->a [f(X) + g(x)] may exist even though neither lim x->a f(x) nor line x->a g(X) exists.


hi thanks for your interest
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Old 10-16-2001, 03:06 AM   #2
notfred
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$f = "lim x->a f(x)";
$g = "line x->a g(X)";
$lim = "x->a [f(X) + g(x)]";

$f =~ s/[ -}]//g;
$g =~ s/[ -}]//g;

if ($f ne ''){print "limit exists\n"}
else{print "limit doesn't exist\n"}

if ($g ne ''){print "limit exists\n"}
else{print "limit doesn't exist\n"}

if ($lim ne ''){print "limit exists\n"}
else{print "limit doesn't exist\n"}
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Old 10-16-2001, 03:06 AM   #3
optimistic
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When adding to infite limits. Fcn's alone are defined as infinite or DNE. When adding to infite you get infite.

Duh! RYan hellO?
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Old 10-16-2001, 03:08 AM   #4
Capn
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exist as in a finite number?

If that's the case then

f(x) = 1/(2-x)

g(x) = 1/(x-2)

x->2 for f(x) would be +/- infinity depending on direction
x->2 for g(x) would also be +/- infinity depending on direction

however f(x)+g(x) equals 0, so x->2 equals 0

Not sure if that's what you're looking for
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Old 10-16-2001, 03:22 AM   #5
optimistic
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thanks guys! you guys care.

im just dumb. this is easy adding infinite limits..........ahhhrrrgghhhhhh..maybe i need sleep
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