Lim x>0 sin 4x - sin 2x / 6x Pliss bantu

Lim x>0 sin 4x - sin 2x / 6x adalah bernilai 1/3. Rumus limit trigonometri

• [tex] \lim \limits_{{x}{\rightarrow}{0}} \frac{sin \: ax}{bx} = \lim \limits_{{x}{\rightarrow}{0}} \frac{ax}{ sin \: bx} = \frac{a}{b} [/tex]

• [tex] \lim \limits_{{x}{\rightarrow}{0}} \frac{tan \: ax}{bx} = \lim \limits_{{x}{\rightarrow}{0}} \frac{ax}{ tan \: bx} = \frac{a}{b} [/tex]

• [tex] \lim \limits_{{x}{\rightarrow}{0}} \frac{sin \: ax}{sin \: bx} = \lim \limits_{{x}{\rightarrow}{0}} \frac{tan \: ax}{tan \: bx} = \frac{a}{b} [/tex]  

• [tex] \lim \limits_{{x}{\rightarrow}{0}} \frac{sin \: ax}{tan \: bx} = \lim \limits_{{x}{\rightarrow}{0}} \frac{tan \: ax}{sin \: bx} = \frac{a}{b} [/tex]  

Jika berbentuk cosinus maka kita ubah dulu menjadi

• cos² ax = 1 – sin² ax
• cos ax = 1 – 2 sin² ½ ax

Pembahasan

[tex] \lim \limits_{{x}{\rightarrow}{0}} \frac{sin \: 4x \: - \: sin \: 2x}{6x}[/tex]

= [tex] \lim \limits_{{x}{\rightarrow}{0}} \frac{sin \: 4x}{6x} - \frac{sin \: 2x}{6x} [/tex]

= [tex]\frac{4}{6} - \frac{2}{6} [/tex]

= [tex]\frac{2}{6}[/tex]

= [tex]\frac{1}{3}[/tex]

Pelajari Lebih Lanjut

Contoh soal lain tentang limit trigonometri

• Lim (x tan x)/(2 cos² x – 2): brainly.co.id/tugas/8875767
• Lim (sin 2x)/(sin 6x): brainly.co.id/tugas/1778468
• Lim (x² + sin² 3x)/(2 tan 2x²): brainly.co.id/tugas/10096707

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Detil Jawaban    

Kelas : 12

Mapel : Matematika  

Kategori : Limit Trigonometri dan Limit Tak Hingga

Kode : 12.2.1

Kata Kunci : Limit trigonometri