Pertanyaan

x → − 2 lim tan 2 ( x + 2 ) ( x 2 − 4 ) sin ( x + 2 ) = ....

$x \to - 2 lim \frac{( x ^{2} - 4 ) sin ( x + 2 )}{tan ^{2} ( x + 2 )} = ....$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Misal sehingga jika maka . Diperoleh: Jadi, jawaban yang tepat adalah E.

Misal sehingga jika maka . Diperoleh:

$begin mathsize 14px style limit as straight x rightwards arrow negative 2 of fraction numerator open parentheses straight x squared minus 4 close parentheses space sin left parenthesis straight x plus 2 right parenthesis over denominator tan squared left parenthesis straight x plus 2 right parenthesis end fraction equals limit as straight x rightwards arrow negative 2 of fraction numerator open parentheses straight x minus 2 right parenthesis left parenthesis straight x plus 2 close parentheses space sin left parenthesis straight x plus 2 right parenthesis over denominator tan squared left parenthesis straight x plus 2 right parenthesis end fraction equals limit as straight y rightwards arrow 0 of fraction numerator straight y left parenthesis straight y plus 4 right parenthesis space sin left parenthesis straight y right parenthesis over denominator tan squared left parenthesis straight y right parenthesis end fraction equals limit as straight y rightwards arrow 0 of open parentheses straight y plus 4 close parentheses space. space limit as straight y rightwards arrow 0 of fraction numerator straight y over denominator tan space left parenthesis straight y right parenthesis end fraction space. space limit as straight y rightwards arrow 0 of fraction numerator sin left parenthesis straight y right parenthesis over denominator tan left parenthesis straight y right parenthesis end fraction equals 4 space. space 1 space. space 1 equals space 4 end style$

Jadi, jawaban yang tepat adalah E.