lim-x-3-tan-x-tan-3-sin-ln-x-2-work-with-the-rule-of-substitution-of-infinitely-small-functions-equivalent-to-a-limit-

Question Number 160865 by vvvv last updated on 08/Dec/21

\lim_{x \to 3} \frac{t a n (x) - t a n (3)}{s i n (l n (x - 2))}

w o r k w i t h t h e r u l e o f

s u b s t i t u t i o n o f i n f i n i t e l y

s m a l l f u n c t i o n s e q u i v a l e n t

t o a l i m i t

Commented by cortano last updated on 08/Dec/21

\lim_{x \to 3} \frac{\tan (x) - \tan (3)}{x - 3} . \lim_{x \to 0} \frac{(x - 3)}{\frac{\sin (\ln (x - 2))}{\ln (x - 2)} . \ln (x - 2)}

= \sec^{2} (3) . \lim_{x \to 3} \frac{x - 3}{\ln (x - 2)}

= \sec^{2} (3) . \lim_{x \to 0} \frac{x}{\ln (x + 1)}

= \sec^{2} (3) . 1 = \sec^{2} (3)

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