Question Number 114088 by bemath last updated on 17/Sep/20

lim_(x→∞) ((2x cot ((2/x))−3cot ((2/x)))/(5x^2 −2x))

Answered by Olaf last updated on 17/Sep/20

= lim_(x→∞) ((1−(1/2)((2/x))^2 )/(((2/x))))[((2x−3)/(5x^2 −2x))] = lim_(x→∞) ((x^2 −2)/(2x))×((2x−3)/(5x^2 −2x)) = lim_(x→∞) ((2x^3 )/(10x^3 )) = (1/5)