calculate lim_(x→0) ((arctan(1+cosx)−arctan(2+x))/x^3 )


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Question Number 56332 by maxmathsup by imad last updated on 14/Mar/19

$c a l c u l a t e {l i m}_{x \to 0} \frac{a r c t a n (1 + c o s x) - a r c t a n (2 + x)}{x^{3}}$
	Answered by kaivan.ahmadi last updated on 07/Apr/19

	$\sim {l i m}_{x \to 0} \frac{1 + c o s x - 2 - x}{x^{3}} =$ ${l i m}_{x \to 0} \frac{- (1 - c o s x) - x}{x^{3}} \sim$ ${l i m}_{x \to 0} \frac{- \frac{x^{2}}{2} - x}{x^{3}} = {l i m}_{x \to 0} \frac{- x - 2}{2 x^{2}} =$ $\frac{- 2}{0^{+}} = - \infty$
	Commented by maxmathsup by imad last updated on 07/Apr/19

	$n o s i r t h i s l i m i t i s r e a l n o t i n f i n t e . . .$
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