Question

[{1 – √(3)cot x}/(2cos x – 1)] for limx→(π/3) = ? 

(a) (4/3) 

(b) – (4/3) 

(c) (2/3) 

(d) – (2/3)

Answer 1

The correct option  (b) – (4/3)  

Explanation:

given: lim_x→(π/3) [{1 – √(3)cotx}/(2cosx – 1)]

∵ lim_x→a [{f(x)}/{g(x)}] = lim_x→a [{f'(x)}/{g'(x)}]

if  lim_x→a [{f(x)}/{g(x)}] = 0

∴  lim_x→(π/3) [{1 – √3[(cosx)/(sin x)]}/(2cosx – 1)]

= lim_x→(π/3) [{sinx – √(3)cos x}/(sin2x – sinx)]

= lim_x→(π/3) [{cosx + √(3)sin x}/(2cos2x – cosx)]

= [{(1/2) + √3(√3/2)}/{2[– (1/2)] – (1/2)}]

= [(4/2)/{– (3/2)}]

= – (4/3)