Lim/x=2 tan(x-2)/(x²+2×-8)² csc (2×-4)
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Penjelasan dengan langkah-langkah:
[tex]lim \: x \: mendekati \: 2 \: \frac{tan \: (x - 2)}{ {( {x}^{2} + 2x - 8})^{2} csc \: (2x - 4)} \\ = \frac{tan \: (x - 2)}{({ {(x + 4)(x - 2))}}^{2}( \frac{1}{cos \: 2(x - 2)}) } \\ = \frac{tan \: (x - 2) (cos \: 2(x - 2)) }{ {((x + 4)(x - 2))}^{2} } \\ = \frac{tan(x - 2) \: (2 \: {cos}^{2}(x - 2)) }{(x + 4)(x + 4)(x - 2)(x - 2)} \\ = \frac{2 \: \frac{sin \: (x - 2)}{cos \: (x - 2)}(cos \: (x - 2)) (cos \: (x - 2))}{(x + 4)(x + 4)(x - 2)(x - 2)} \\ = \frac{2 \: sin \: (x - 2)(cos \: (x - 2))}{(x + 4)(x + 4)(x - 2)(x - 2)} \\ = \frac{2}{(x + 4)(x + 4)} \\ = \frac{2}{(2 + 4)(2 + 4)} \\ = \frac{2}{36} \\ = \frac{1}{18} [/tex]
