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Nilai x→9lim​x+3x​−182x2−162​ adalah ...

Pertanyaan

Nilai begin mathsize 14px style 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 style adalah ...

  1. 36space space   

  2. 24space space

  3. 18space space

  4. 6space space

  5. 3space space

Pembahasan:

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

Jawaban terverifikasi

Dijawab oleh:

Terakhir diupdate 06 Oktober 2021

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