Question: Show that f(x)= (x^2)/((x^2)+1) is continuous on [0,infinity). Is it uniformly continuous?(adsbygoogle = window.adsbygoogle || []).push({});

My attempt: So I know that continuity is defined as

"given any Epsilon, and for all x contained in A, there exists delta >0 such that if y is contained in A and abs(y-x)<delta, then abs(f(x)-f(y))<Epsilon.

So i tried expanding the function, but still can not find the values for delta that make this continuous on [0,infinity). Any ideas?

Also, it is NOT uniformly continuous correct?

Thanks!

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# Real Analysis: Continuity and Uniform Continuity

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