tentukan nilai lim x -> 0 cos ^2 5x - 1 / 4x tan 2x
Penjelasan dengan langkah-langkah:
[tex] = \lim \limits_{x \to0} \frac{ \cos {}^{2} (5x) - 1}{4x \tan(2x) } [/tex]
[tex] = \lim \limits_{x \to0} \frac{ - \sin {}^{2} (5x) }{4x \tan(2x) } [/tex]
[tex] = \lim \limits_{x \to0} \frac{ - \sin(5x) }{4x} \times \lim \limits_{x \to0} \frac{ \sin(5x) }{ \tan(2x) } [/tex]
[tex] = \frac{ - 5}{4} \times \frac{5}{2} [/tex]
[tex] = - \frac{25}{8} [/tex]
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