Question Number 114405 by bemath last updated on 19/Sep/20

    lim_(x→0)  ((x tan x)/( (√3) cos x−sin ^2 x−(√3))) ?

Answered by bobhans last updated on 19/Sep/20

 lim_(x→0)  ((x tan x)/( (√3)(cos x−1)−sin ^2 x)) =  lim_(x→0)  (x^2 /( (√3)(1−(x^2 /2)−1)−x^2 )) =  lim_(x→0)  (x^2 /(x^2 (−((√3)/2)−1))) = ((−2)/( (√3)+2)) = ((−2(2−(√3)))/(4−3))                                         = 2(√3)−2

Commented bybemath last updated on 19/Sep/20

gave kudos ✓≎

Answered by Dwaipayan Shikari last updated on 19/Sep/20

lim_(x→0) ((xtanx)/( (√3)(cosx−1)−sin^2 x))=(x^2 /(−2(√3)sin^2 (x/2)−4sin^2 (x/4)cos^2 (x/2)))  =(x^2 /(((−(√3))/2)x^2 −x^2 ))=−(2/( (√3)+2))=2((√3)−2)