Penjelasan dengan langkah-langkah:
[tex] = \lim \limits_{x \to0} \frac{ \tan {}^{4} (6x) }{ {(x \sin(4x) )}^{2} } [/tex]
[tex] = \lim \limits_{x \to0} \frac{ \tan {}^{4} (6x) }{ {x}^{2} \sin {}^{2} (4x) } [/tex]
[tex] \: [/tex]
Jabarkan.
[tex] = \lim \limits_{x \to0} (\frac{ \tan {}^{2} (6x) }{ {x}^{2} } \times \frac{ \tan {}^{2} (6x) }{ \sin {}^{2} (4x) } )[/tex]
[tex] = \lim \limits_{x \to0} \frac{ \tan {}^{2} (6x) }{ {x}^{2} } \times \lim \limits_{x \to0} \frac{ \tan {}^{2} (6x) }{ \sin {}^{2} (4x) } [/tex]
[tex] = \lim \limits_{x \to0} {( \frac{ \tan(6x) }{x} )}^{2} \times \lim \limits_{x \to0} {( \frac{ \tan(6x) }{ \sin(4x) } )}^{2} [/tex]
[tex] = {(\lim \limits_{x \to0} \frac{ \tan(6x) }{x} )}^{2} \times {(\lim \limits_{x \to0} \frac{ \tan(6x) }{ \sin(4x) } )}^{2} [/tex]
[tex] = {( \frac{6}{1} )}^{2} \times {( \frac{6}{4} )}^{2} [/tex]
[tex] = {6}^{2} \times {( \frac{3}{2} )}^{2} [/tex]
[tex] = 36 \times \frac{9}{4} [/tex]
[tex] = 9\times 9[/tex]
[tex] = 81[/tex]
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