Question Number 114079 by bemath last updated on 17/Sep/20

Answered by john santu last updated on 17/Sep/20

setting (1/x) = m ∧m→0  lim_(m→0)  ((m^2  sin 4m)/((1−cos 2m)sin m)) =  lim_(m→0)  ((m^2  sin 4m)/(2sin ^2 m. sin m)) = (4/2) = 2

Answered by Olaf last updated on 17/Sep/20

= lim_(x→∞) ((4/x)/((1−(1−(1/2)((2/x))^2 ))x^2 (1/x)))  = lim_(x→∞) ((4/x)/(((1/2)((2/x))^2 )x^2 (1/x)))  = lim_(x→∞) ((4/x)/(((2/x^2 ))x)) = (4/2) = 2