x→3lim​x2+9x−36x2−x−6​​= ....

Pertanyaan

begin mathsize 14px style limit as straight x rightwards arrow 3 of square root of fraction numerator straight x squared minus straight x minus 6 over denominator straight x squared plus 9 straight x minus 36 end fraction end root equals end style ....

  1. 1

  2. begin mathsize 14px style 1 half end style 

  3. begin mathsize 14px style 1 half square root of 2 end style 

  4. begin mathsize 14px style 1 third end style 

  5. begin mathsize 14px style 1 third square root of 3 end style 

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Perhatikan bahwa jika dilakukan substitusi = 3, maka didapatkan hasil undefined .
Sehingga perlu dicari cara lain untuk mencari nilai limitnya.

Perhatikan bahwa

begin mathsize 14px style limit as straight x rightwards arrow 3 of square root of fraction numerator straight x squared minus straight x minus 6 over denominator straight x squared plus 9 straight x minus 36 end fraction end root equals square root of limit as straight x rightwards arrow 3 of fraction numerator straight x squared minus straight x minus 6 over denominator straight x squared plus 9 straight x minus 36 end fraction end root equals square root of limit as straight x rightwards arrow 3 of fraction numerator open parentheses straight x minus 3 close parentheses open parentheses straight x plus 2 close parentheses over denominator open parentheses straight x minus 3 close parentheses open parentheses straight x plus 12 close parentheses end fraction end root equals square root of limit as straight x rightwards arrow 3 of fraction numerator straight x plus 2 over denominator straight x plus 12 end fraction end root equals square root of fraction numerator 3 plus 2 over denominator 3 plus 12 end fraction end root equals square root of 5 over 15 end root equals square root of 1 third end root equals fraction numerator 1 over denominator square root of 3 end fraction equals fraction numerator 1 over denominator square root of 3 end fraction times fraction numerator square root of 3 over denominator square root of 3 end fraction equals 1 third square root of 3 end style 

Jadi, jawaban yang tepat adalah E.

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