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let $f_1:\left(0, \frac{\pi}{2}\right), f_1(x)=\left(\frac{\ln\left(\cos^2(x)\right)}{\ln\left(x^3\right)}\right)$

$\rightarrow$ The ln function is only used for an interval with positive values so I assume it is continuous.

$$|f(x) - f(x_0)|$$ $$\left|\frac{\ln\left(\cos^2(x)\right)}{\ln\left(x^3\right)}- \frac{\ln\left(\cos^2(x_0)\right)}{\ln\left(x_0^3\right)}\right|$$

Question: How can I go on to get $|x-x_0|$ to have my $\delta$ and finally to define the $\epsilon$.

I appreciate every hint.

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  • $\begingroup$ The domain is $(0,1)\cup(1,\frac \pi 2$ $\endgroup$ Dec 27, 2016 at 18:40
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    $\begingroup$ Please tell me you did not "cancel" the symbols $\frac{\ln}{\ln}$ in the fraction going from the 2nd to the 3rd displayed expression. That's certainly not a legal step in simplifying an expression! $\endgroup$
    – MPW
    Dec 27, 2016 at 18:45
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    $\begingroup$ Also notice your $f_1$ became $f$. I would suggest dropping the subscript altogether, it is meaningless here. $\endgroup$
    – MPW
    Dec 27, 2016 at 18:47

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