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Evaluate lim(xto(pi)/(6)) (2-sqrt(3)cosx...

Evaluate `lim_(xto(pi)/(6)) (2-sqrt(3)cosx-sinx)/((6x-pi)^(2)).`

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`underset(xto(pi)/(6))lim(2-sqrt(3)cosx-sinx)/((6x-pi)^(2))" "`(0/0 from)
`=underset(xto(pi)/(6))lim2xx(1-((sqrt(3))/(2)cosx+1/2sinx))/((6x-pi)^(2))`
`=underset(xto(pi)/(6))lim2xx(1-cos(x-(pi)/(6)))/(36(x-(pi)/(6))^(2))`
`=underset(xto(pi)/(6))lim(2sin^(2)(x/2-pi/12))/(18xx4(x/2-pi/12)^(2))`
`=(1)/(36)(underset(xto(pi)/(6))lim(sin(x/2-pi/12))/((x/2-pi/12)))^(2)\=(1)/(36)`
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