lim (x→π) (sin 4(x-π)/[(x-π)+tan(x-π)] = ...
A. 1
...

Question

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

S. Sofi · Accepted Answer

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.

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

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