Question Number 105157 by bramlex last updated on 26/Jul/20

lim_(x→(π/6))  ((cos ^2 (((3x)/2))−sin x)/(sin x+(√3) cos x−2)) ?

Answered by bramlex last updated on 26/Jul/20

cos ^2 (((3x)/2)) = (1/2)(cos 3x+1)  lim_(x→π/6)  (((1/2)(cos 3x+1)−sin x)/(sin x+(√3) cos x−2))  lim_(x→π/6) (((1/2)(−3sin 3x)−cos x)/(cos x−(√3) sin x))  =(((3/2)+((√3)/2))/(((√3)/2)−((√3)/2))) = ∞ (DNE )