Question

tolong dijawab soal penyelesaian limit ini dong

Answer 1

Verified answer

Jawaban:

[tex] \frac{3}{2} [/tex]

Penjelasan dengan langkah-langkah:

Cara 1: Gunakan sifat [tex]\bold{\lim\limits_{x \to 0} \frac{\sin (m x)}{n x} = \frac{m}{n}}[/tex]

[tex]\begin{aligned}\lim\limits_{x \to 0} & \frac{ \sin(x) + \sin(8x) }{6x} \\\lim\limits_{x \to 0} & \frac{ \sin(x) }{6x} + \frac{ \sin(8x) }{6x} \\& = \frac{1}{6} + \frac{8}{6} \\ & = \frac{9}{6} \\& = \frac{3}{2} \end{aligned}[/tex]

Cara 2: Gunakan turunan

[tex]\begin{aligned}\lim\limits_{x \to 0} & \frac{ \sin(x) + \sin(8x) }{6x} \\\lim\limits_{x \to 0} & \frac{ \frac{d}{dx} (\sin(x) + \sin(8x))}{ \frac{d}{dx} 6x} \\\lim\limits_{x \to 0} & \frac{ \cos(x) + 8 \cos(8x) }{6} \\& = \frac{ \cos(0) + 8 \cos(8(0)) }{6} \\& = \frac{1 + 8(1)}{6} \\ & = \frac{1 + 8}{6} \\ & = \frac{9}{6} \\& = \frac{3}{2} \end{aligned}[/tex]

[tex] \\ [/tex]

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Answer 2

Limit Trigonometri

[Metode L'Hopital]

..

[tex]\displaystyle \lim_{x \to 0} \left( \frac{sin~(x) + sin~(8x)}{6x}\right)[/tex]

Penyelesaian Soal

[tex]\begin{aligned}\displaystyle \lim_{x \to 0} & \left( \frac{\frac{d}{dx}(sin~(x) + sin~(8x))}{\frac{d}{dx}6x}\right) \\ \displaystyle \lim_{x \to 0} & \left( \frac{cos~(x) + 8cos~(8x)}{6}\right) \\= \: \: & \: \: \frac{1 + 8 (1)}{6} \\ = \: \: & \: \: \frac{1 + 8}{6} \\= \: \: & \: \: \frac{9}{6} \\= \: \: & \: \: \boxed{\bold{\underline{ \frac{3}{2}}}} \end{aligned}[/tex]

[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alf'at | 01 - 08 - 2023}}[/tex]