Proving Continuity of f(x,y) = y/(1+x2) Using Delta-Epsilon Bound

trap101
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Use the delta-epsilon definition to prove f(x,y) = y/(1+x2) is continuous at (0,0)Attempts:So I'm doing some work and my main issue is finding a bound for the denominator of 1+x2:

So work wise I have something looking like:

\delta/(|1| + |x2| ). How could I found a good bound?
 
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trap101 said:
Use the delta-epsilon definition to prove f(x,y) = y/(1+x2) is continuous at (0,0)

Attempts:

So I'm doing some work and my main issue is finding a bound for the denominator of 1+x2:

So work wise I have something looking like:

\delta/(|1| + |x2| ). How could I found a good bound?
An lower bound for 1+x2 is definitely 1.

That makes and upper bound of 1 for 1/(1+x2) .
 
thanks
 
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