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Evaluate: ("lim")(h->0)(2[sqrt(3)sin(pi/...

Evaluate: `("lim")_(h->0)(2[sqrt(3)sin(pi/6+h)-cos(pi/6+h)])/(sqrt(3)h(sqrt(3)cosh-sinh)`

Text Solution

Verified by Experts

The correct Answer is:
`4//3`
`underset(hto0)lim(2[sqrt(3)sin((pi)/(6)+h)-cos((pi)/(6)+h)])/(sqrt(3)h(sqrt(3)cosh-sinh))`
`underset(hto0)lim((4)/sqrt(3)[sqrt(3)/(2)sin((pi)/(6)+h)-(1)/(2)cos((pi)/(6)+h)])/(h(sqrt(3)cosh-sinh))`
`=underset(hto0)lim(4)/(sqrt(3))xx(sinh)/(h)(1)/((sqrt(3)cosh-sinh))=4/3`
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