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

[trap101]

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?

 

[SammyS]

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) .

 

[trap101]

thanks