[tex] \: [/tex]
[tex] \displaystyle \rm \lim_{x \to0} \: \frac{1 - \cos^{3} (x) }{3x \tan(3x) } = \cdots[/tex]
Penyelesaian:
[tex]\displaystyle \sf \lim_{x \to0} \: \frac{1 - \cos^{3} (x) }{3x \tan(3x) } = \displaystyle \sf \lim_{x \to0} \frac{( \cos x )(1 + \cos x + \cos {}^{2}x) }{3 \times \tan 3x } [/tex]
[tex] \tt= \displaystyle \sf \lim_{x \to0} \frac{2 \sin \frac{1}{2}x }{3x}×\displaystyle \sf \lim_{x \to0} \frac{ \sin \frac{1}{2}x }{ \tan3x }×\displaystyle \sf \lim_{x \to0}(1 + \cos x + \cos {}^{2}x)[/tex]
[tex] = \sf \frac{2× \frac{1}{2} }{3}× \frac{1}{ \frac{2}{3} }×(1 + \cos(0) + \cos {}^{2} (0))[/tex]
[tex] = \sf \frac{1}{3}× \frac{1}{6}×(1 + 1 + 1)[/tex]
[tex] = {\bold{\frac{1}{6}}}[/tex]
Kesimpulan:
Maka, hasilnya adalah 1/6.
[tex]{\color{red}{\bold{[F]{\color{black}{x}{\color{blue}{[M]}}}}}}[/tex]
Penjelasan dengan langkah-langkah:
lim = 1 - cos³ (x)/3x Tan (3x)
x → 0
2 sin ½x/3x x. sin ½x/tan 3x. x (1 + cos x + cos²x)
1/3 x 1/6 x (1 + 1 + 1)
1/18 x 3
1/6
[answer.2.content]
