Question

$\lim_{x \to 3} \frac{tg3-tgx}{ln3-lnx}$
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Answer 1

$\lim\limits _{x \to 3}\frac{tg3-tgx}{ln3-lnx}=\Big [\, \frac{0}{0}\, \Big ]=\lim\limits _{x \to 3}\frac{(tg3-tgx)'}{(ln3-lnx)'}=\lim\limits _{x \to 3}\frac{0-\frac{1}{cos^2x}}{0-\frac{1}{x}}=\lim\limits _{x \to 3}\frac{x}{cos^2x}=\frac{3}{cos^23}$