(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

2. Relevant equations

$$a^2-b^2=(a-b)(a+b)$$

3. The attempt at a solution

$$a^2=\sqrt{1-x_2^2}\,\,\, ,\ \ b^2=\sqrt{1-x_1^2}$$

$$|a^2-b^2|=\left| \sqrt{1-x_2^2}-\sqrt{1-x_1^2} \right|=\left| \sqrt[4]{1-x_2^2} - \sqrt[4]{1-x_1^2} \right|\cdot\left| \sqrt[4]{1-x_2^2} + \sqrt[4]{1-x_1^2} \right|$$

I have to reach:

$$\left| \sqrt{y_2} - \sqrt{y_1} \right| \leq \sqrt{\sqrt{1-x_2^2} - \sqrt{1-x_1^2} }$$

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# Homework Help: Complex uniform continuity

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