Soal No 2 matematika POLMED 2019

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Soal No 2 matematika POLMED 2019

Soal No 2 matematika POLMED 2019

Jawaban:

D. 1/2

Penjelasan dengan langkah-langkah:

lim x->0 (sin 3x sin 2x)/ (12 x² cos3x) =

ubah sususnan

lim x->0 (sin 3x sin 2x)/(cos 3x . x² . 12) =

kita ubah sin 3x/ cos 3x = tan 3x

lim x->0 (tan 3x sin 2x)/(x² . 12) =

kita potong-potong agar sesuai aturan limit trigonometri

lim x->0 ((tan 3x)/x) . ((sin 2x)/x) . (1/12) =

3 . 2 . 1/12 = 6/12 = 1/2

Jawab:

Penjelasan dengan langkah-langkah:

lim_{x to 0} frac{sin3x.sin2x}{12x^2.cos3x}\\=frac{1}{12} lim_{x to 0} frac{sin3x}{x}. lim_{x to 0} frac{sin2x}{x}. lim_{x to 0} frac{1}{cos3x}\\=frac{1}{12}.3.2.frac{1}{cos0}\\=frac{1}{2}