Pertanyaan

Nilai x → 9 lim x + 3 x − 18 2 x 2 − 162 adalah ...

Nilai $x \to 9 lim \frac{2 x ^{2} - 162}{x + 3 x - 18}$ adalah ...

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E. Lestari

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Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Pembahasan

jadi, jawaban yang tepat adalah B.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row blank blank cell limit as straight x rightwards arrow 9 of fraction numerator 2 straight x squared minus 162 over denominator straight x plus 3 square root of straight x minus 18 end fraction end cell row blank equals cell limit as straight x rightwards arrow 9 of fraction numerator 2 open parentheses straight x squared minus 81 close parentheses over denominator straight x plus 3 square root of straight x minus 18 end fraction rightwards arrow keluarkan space faktor space 2 end cell row blank equals cell limit as straight x rightwards arrow 9 of fraction numerator 2 open parentheses straight x squared minus 81 close parentheses over denominator straight x plus 6 square root of 3 minus 3 square root of straight x minus 18 end fraction rightwards arrow tulis space square root of 3 sebagai space selisih end cell row blank equals cell limit as straight x rightwards arrow 9 of fraction numerator 2 open parentheses straight x minus 9 close parentheses open parentheses straight x plus 9 close parentheses over denominator straight x plus 6 square root of 3 minus 3 square root of straight x minus 18 end fraction end cell row blank equals cell limit as straight x rightwards arrow 9 of fraction numerator 2 open parentheses straight x minus 9 close parentheses open parentheses straight x plus 9 close parentheses over denominator square root of straight x open parentheses square root of straight x plus 6 close parentheses minus 3 square root of straight x minus 18 end fraction rightwards arrow keluarkan space faktor square root of straight x end cell row blank equals cell limit as straight x rightwards arrow 9 of fraction numerator 2 open parentheses straight x minus 9 close parentheses open parentheses straight x plus 9 close parentheses over denominator square root of straight x open parentheses square root of straight x plus 6 close parentheses minus 3 open parentheses square root of straight x plus 6 close parentheses end fraction end cell row blank equals cell limit as straight x rightwards arrow 9 of fraction numerator 2 open parentheses straight x minus 9 close parentheses open parentheses straight x plus 9 close parentheses over denominator open parentheses square root of straight x plus 6 close parentheses open parentheses square root of straight x minus 3 close parentheses end fraction end cell row blank equals cell limit as straight x rightwards arrow 9 of fraction numerator 2 open parentheses square root of straight x minus 3 close parentheses open parentheses square root of straight x plus 3 close parentheses open parentheses straight x plus 9 close parentheses over denominator open parentheses square root of straight x plus 6 close parentheses open parentheses square root of straight x minus 3 close parentheses end fraction end cell row blank equals cell limit as straight x rightwards arrow 9 of fraction numerator 2 up diagonal strike open parentheses square root of straight x minus 3 close parentheses end strike open parentheses square root of straight x plus 3 close parentheses open parentheses straight x plus 9 close parentheses over denominator open parentheses square root of straight x plus 6 close parentheses up diagonal strike open parentheses square root of straight x minus 3 close parentheses end strike end fraction end cell row blank equals cell limit as straight x rightwards arrow 9 of fraction numerator 2 open parentheses square root of straight x plus 3 close parentheses open parentheses straight x plus 9 close parentheses over denominator open parentheses square root of straight x plus 6 close parentheses end fraction end cell row blank equals cell fraction numerator 2 open parentheses square root of 9 plus 3 close parentheses open parentheses 9 plus 9 close parentheses over denominator open parentheses square root of 9 plus 6 close parentheses end fraction end cell row blank equals cell fraction numerator 2 open parentheses 3 plus 3 close parentheses open parentheses 18 close parentheses over denominator 3 plus 6 end fraction end cell row blank equals cell 216 over 9 end cell row blank equals 24 end table end style$

jadi, jawaban yang tepat adalah B.