Nilai dari x → 0 lim ​ cos 5 x − cos 3 x cos 4 x − 1 ​ = ...

Pembahasan

Ingat! x → 0 lim ​ sin b x sin a x ​ = x → 0 lim ​ sin b x a x ​ = b a ​ cos 2 x = 1 − 2 ⋅ sin 2 x cos A − cos B = − 2 ⋅ sin 2 1 ​ ( A + B ) ⋅ sin 2 1 ​ ( A − B ) Perhatikan perhitungan berikut lim x → 0 ​ c o s 5 x − c o s 3 x c o s 4 x − 1 ​ ​ = = = = = ​ lim x → 0 ​ − 2 ⋅ s i n 2 1 ​ ( 5 x + 3 x ) ⋅ s i n 2 1 ​ ( 5 x − 3 x ) ( 1 − 2 ⋅ s i n 2 2 x ) − 1 ​ lim x → 0 ​ − 2 ⋅ s i n 4 x ⋅ s i n x − 2 ⋅ s i n 2 2 x ​ lim x → 0 ​ s i n 4 x ⋅ s i n x s i n 2 x ⋅ s i n 2 x ​ 4 ⋅ 1 2 ⋅ 2 ​ 1 ​ Oleh karena itu, jawaban yang benar adalah B.