lim (x→π) (sin 4(x-π)/[(x-π)+tan(x-π)] = ... A. 1 B. 2 C. 4 D. 6 E. 8

Jawaban yang benar adalah B. 2 Pembahasan Ingat! 1. lim (x → a) (f(x)/g(x)) = (lim (x → a) f(x))/(lim (x → a) g(x)) 2. lim (x → a) (f(x) ± g(x)) = (lim (x → a) f(x)) ± (lim (x → a) g(x)) 3. lim (x → a) [(sin (k . (x – a)))/(x – a)] = k 4. lim (x → a) [(tan (k . (x – a)))/(x – a)] = k lim (x → π)(sin 4(x – π)/[(x – π) + tan(x – π)] = lim (x → π) (sin 4(x – π)/[(x – π) + tan(x – π)] × {[1/(x – π)]/[1/(x – π)]} = lim (x → π) {[(sin4(x–π)] × [1/(x – π)]} /{[(x – π) + tan(x – π)] × [1/(x – π)]} = lim (x → π) [(sin4(x – π))/(x – π)] / {[((x – π))/(x – π)] + [(tan(x – π))/(x – π)]} = [4]/[1 + 1] = 4/2 = 2 Jadi, jawaban yang tepat adalah B.