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Let \(\displaystyle f:R^2 \rightarrow R\) by

\(\displaystyle f(x) = \frac{x_1^2x_2}{x_1^4+x_2^2}\) for \(\displaystyle x \not= 0\)

Prove that for each \(\displaystyle x \in R\), \(\displaystyle f(tx)\) is a continuous function of \(\displaystyle t \in R\)

(\(\displaystyle R\) is the real numbers, I'm not sure how to get it to look right).

I am letting \(\displaystyle t_0 \in R\) and \(\displaystyle \epsilon > 0\) then trying to find a \(\displaystyle \delta > 0\) so \(\displaystyle |f(t) - f(t_0)| < \epsilon\) whenever \(\displaystyle |t - t_0| < \delta\) I am stuck trying to find the delta what will work, in trying to find it I am unable to simplify out \(\displaystyle |t - t_0|\) to use. Am I missing something really obvious here? Any help appreciated.