Question

lim x tends to π/3 √3-tanx /π-3x. Without hospital rule

Answer 1

Answer:

.. lim (x→π/3) [ ( √3 - tan x ) / ( π - 3x ) ]

= lim (x→π/3) {[( tan π/3 - tan x )/( 1 + tan π/3 tan x )] / (π-3x) }•( 1 + tan π/3 tan x)

= lim (x→π/3) { [ tan (π/3 - x) / (π - 3x ) ] • ( 1 + √3. tan x ) }

= lim (x→π/3) { [ tan (π/3 - x) ] / [ 3 (π/3 - x) ] } • ( 1 + √3. tan π/3 )

= (1/3) • { lim ( h → 0 ) [ ( tan h ) / ( h ) ] } • ( 1 + √3.√3 ) , .... where h = π/3 - x

= (1/3) • { 1 } • ( 1 + 3 )

= 4/ 3 ............................................ Ans.

________________________

Step-by-step explanation: