ryo0071
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Okay so the question is:
Let $$f:R^2 \rightarrow R$$ by
$$f(x) = \frac{x_1^2x_2}{x_1^4+x_2^2}$$ for $$x \not= 0$$
Prove that for each $$x \in R$$, $$f(tx)$$ is a continuous function of $$t \in R$$
($$R$$ is the real numbers, I'm not sure how to get it to look right).
I am letting $$t_0 \in R$$ and $$\epsilon > 0$$ then trying to find a $$\delta > 0$$ so $$|f(t) - f(t_0)| < \epsilon$$ whenever $$|t - t_0| < \delta$$ I am stuck trying to find the delta what will work, in trying to find it I am unable to simplify out $$|t - t_0|$$ to use. Am I missing something really obvious here? Any help appreciated.
Let $$f:R^2 \rightarrow R$$ by
$$f(x) = \frac{x_1^2x_2}{x_1^4+x_2^2}$$ for $$x \not= 0$$
Prove that for each $$x \in R$$, $$f(tx)$$ is a continuous function of $$t \in R$$
($$R$$ is the real numbers, I'm not sure how to get it to look right).
I am letting $$t_0 \in R$$ and $$\epsilon > 0$$ then trying to find a $$\delta > 0$$ so $$|f(t) - f(t_0)| < \epsilon$$ whenever $$|t - t_0| < \delta$$ I am stuck trying to find the delta what will work, in trying to find it I am unable to simplify out $$|t - t_0|$$ to use. Am I missing something really obvious here? Any help appreciated.