HW help in calc: SOLVED

[optimistic]

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

 

[notfred]

$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"}

 

[optimistic]

When adding to infite limits. Fcn's alone are defined as infinite or DNE. When adding to infite you get infite.

Duh! RYan hellO?

 

[Capn]

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

 

[optimistic]

thanks guys! you guys care.

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