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Lim (sin 4x + sin 2x)/(3x cos x) = 2

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]

Pembahasan

[tex] \lim \limits_{{x}{\rightarrow}{0}} \frac{sin \: 4x \: + \: sin \: 2x}{3x \: cos x} [/tex]

[tex]= \lim \limits_{{x}{\rightarrow}{0}} \frac{sin \: 4x \: + \: sin \: 2x}{3x} \cdot \frac{1}{cos x} [/tex]

[tex]= \lim \limits_{{x}{\rightarrow}{0}} \left(\frac{sin \: 4x}{3x} + \frac{sin \: 2x}{3x} \right) \cdot \frac{1}{cos x} [/tex]

[tex]= \left(\frac{4}{3} + \frac{2}{3} \right) \cdot \frac{1}{cos 0} [/tex]

[tex]= \frac{6}{3} \cdot \frac{1}{1} [/tex]

= 2

Pelajari lebih lanjut

Contoh soal lain tentang limit trigonometri

• Nilai Lim x mendekati 0 sin 7x/4x: brainly.co.id/tugas/30478925
• Nilai limit x mendekati 0 dari sin 8x . tan x/ 1 – cos 4x: brainly.co.id/tugas/30232173
• Lim (x tan x)/(2 cos² x – 2): brainly.co.id/tugas/8875767

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Detil Jawaban      

Kelas : 12

Mapel : Matematika Peminatan

Kategori : Limit Trigonometri dan Limit Tak Hingga

Kode : 12.2.1