lim 2x^2 + x : sin x dimana x→0 sama dengan... A. -1 B. 0 C. 1 D. 2 E. 3

Lim 2x^2 + x : sin x dimana x→0 sama dengan 1

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{2x^{2} + x}{sin \: x} [/tex]

[tex]= \lim \limits_{{x}{\rightarrow}{0}} \frac{x(2x + 1)}{sin \: x} [/tex]

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

[tex]= 1 \cdot (2(0) + 1) [/tex]  

[tex]= 1 \cdot 1 [/tex]

= 1

Jawaban C

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