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lim(x->pi/6)(2-sqrt(3)cosx-sinx)/((6x-pi...

`lim_(x->pi/6)(2-sqrt(3)cosx-sinx)/((6x-pi)^2)`

Text Solution

Verified by Experts

Applying L hospital rule, differentiating numerator and denominator separately we get
=>` lim_(x->((pi)/6)) (sqrt(3)sin(x)-cos(x))/(12(6x-(pi)))`
applying L hospital rule again we get
=>` lim_(x->((pi)/6)) (sqrt(3)cos(x)+sin(x))/(72)`
=>`(sqrt3 cos((pi)/6)+sin((pi)/6))/72=1/(36)`
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