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= Lim (2 cos 1/2 (x + a) sin 1/2 (x - a)) / (x - a)
= Lim 2 cos 1/2 (x + a) . (Sin 1/2 (x - a))/(x - a)
= 2 cos 1/2 (a + a) . 1/2
= 2 . 1/2 . Cos 1/2 (2a)
= Cos a
2) Lim (x - 3)/(√x - √3)
= Lim (√x + √3)(√x - √3)/(√x - √3)
= Lim (√x + √3)
= √3 + √3
= 2√3