Question

Find the limit as delta(x) approaches 0, f(x)=[sin[(pi/6)+delta(x)]-(1/2)]/delta(x)

Answer 1

use\[\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta\]

Answer 2

[(sin pi/6)(cos delta x)+(cos pi/6)(sin delta x)-(1/2)]/ delta x

Answer 3

[(1/2)(cos delta x)+(sqrt{3}\2)(sin delta x)-(1/2)]/ delta x

Answer 4

lost

Answer 5

sqrt{3}/2