pakee cara
Nilai dari [tex]\displaystyle{ \lim_{x \to 0} \frac{cosx.tan3x.cos2x}{sin4x-6xtan3x} }[/tex] adalah [tex]\displaystyle{ \boldsymbol{\frac{3}{4} }}[/tex].
PEMBAHASAN
Teorema pada limit adalah sebagai berikut :
[tex](i)~\lim\limits_{x \to c} f(x)=f(c)[/tex]
[tex](ii)~\lim\limits_{x \to c} kf(x)=k\lim\limits_{x \to c} f(x)[/tex]
[tex](iii)~\lim\limits_{x \to c} [f(x)\pm g(x)]=\lim\limits_{x \to c} f(x)\pm\lim\limits_{x \to c} g(x)[/tex]
[tex](iv)~\lim\limits_{x \to c} [f(x)\times g(x)]=\lim\limits_{x \to c} f(x)\times\lim\limits_{x \to c} g(x)[/tex]
[tex](v)~\lim\limits_{x \to c} \left [ \frac{f(x)}{g(x)} \right ]=\frac{\lim\limits_{x \to c} f(x)}{\lim\limits_{x \to c} g(x)}[/tex]
[tex](vi)~\lim\limits_{x \to c} \left [ f(x) \right ]^n=\left [ \lim\limits_{x \to c} f(x) \right ]^n[/tex]
Rumus untuk limit fungsi trigonometri :
[tex]\displaystyle{(i)~\lim\limits_{x \to 0} \frac{sinax}{bx}=\lim\limits_{x \to 0} \frac{tanax}{bx}=\frac{a}{b} }[/tex]
[tex]\displaystyle{(ii)~\lim\limits_{x \to 0} \frac{ax}{sinbx}=\lim\limits_{x \to 0} \frac{ax}{tanbx}=\frac{a}{b}}[/tex]
[tex]\displaystyle{(iii)~\lim\limits_{x \to 0} \frac{sinax}{sinbx}=\lim\limits_{x \to 0} \frac{tanax}{tanbx}=\frac{a}{b} }[/tex]
[tex]\displaystyle{(iv)~\lim\limits_{x \to a} \frac{sin(x-a)}{(x-a)}=\lim\limits_{x \to a} \frac{tan(x-a)}{(x-a)}=1 }[/tex]
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DIKETAHUI
[tex]\displaystyle{ \lim_{x \to 0} \frac{cosx.tan3x.cos2x}{sin4x-6xtan3x}= }[/tex]
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DITANYA
Tentukan nilai limitnya.
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PENYELESAIAN
[tex]\displaystyle{ \lim_{x \to 0} \frac{cosx.tan3x.cos2x}{sin4x-6xtan3x} }[/tex]
[tex]\displaystyle{=\lim_{x \to 0} \frac{cosx.tan3x.cos2x}{sin4x-6xtan3x}\times\frac{\frac{1}{x}}{\frac{1}{x}} }[/tex]
[tex]\displaystyle{=\lim_{x \to 0} \frac{\frac{cosx.tan3x.cos2x}{x}}{\frac{sin4x-6xtan3x}{x}}}[/tex]
[tex]\displaystyle{= \frac{\lim\limits_{x \to 0} \frac{ cosx.tan3x.cos2x}{x}}{\lim\limits_{x \to 0} \frac{sin4x-6xtan3x}{x}}}[/tex]
[tex]\displaystyle{= \frac{\lim\limits_{x \to 0} \frac{tan3x}{x}\times\lim\limits_{x \to 0} (cosx.cos2x)}{\lim\limits_{x \to 0} \frac{sin4x}{x}-\left ( \lim\limits_{x \to 0} \frac{tan3x}{x}\times\lim\limits_{x \to 0} 6x \right )}}[/tex]
[tex]\displaystyle{= \frac{3\times(cos0.cos2(0))}{4-\left ( 3\times6(0) \right )}}[/tex]
[tex]\displaystyle{= \frac{3\times1}{4-0}}[/tex]
[tex]\displaystyle{= \frac{3}{4}}[/tex]
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KESIMPULAN
Nilai dari [tex]\displaystyle{ \lim_{x \to 0} \frac{cosx.tan3x.cos2x}{sin4x-6xtan3x} }[/tex] adalah [tex]\displaystyle{ \boldsymbol{\frac{3}{4} }}[/tex].
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PELAJARI LEBIH LANJUT
- Limit fungsi trigonometri : https://brainly.co.id/tugas/41998117
- Limit trigonometri : https://brainly.co.id/tugas/38915095
- Limit trigonometri : https://brainly.co.id/tugas/30308496
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DETAIL JAWABAN
Kelas : 11
Mapel: Matematika
Bab : Limit Fungsi
Kode Kategorisasi: 11.2.8
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