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Nilai dari x→3lim​x2+7​−4x2−9​ adalah ...

Pertanyaan

Nilai dari begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator square root of x squared plus 7 end root minus 4 end fraction end style adalah ...

  1. begin mathsize 14px style 3 end style 

  2. begin mathsize 14px style 4 end style 

  3. begin mathsize 14px style 6 end style 

  4. begin mathsize 14px style 8 end style 

  5. begin mathsize 14px style 9 end style 

B. Hary

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Diketahui:

Limit fungsi pembagian dengan penyebut berbentuk akar, yaitu begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator square root of x squared plus 7 end root minus 4 end fraction end style.

Hasil substutusi nilai x ke fungsi f left parenthesis x right parenthesis adalah 0 over 0 sehingga penyelesaian limit fungsi tersebut dapat menggunakan metode mengalikan dengan akar sekawan.

Operasikan bentuk limit dengan akar sekawan seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator square root of x squared plus 7 end root minus 4 end fraction end cell equals cell limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator square root of x squared plus 7 end root minus 4 end fraction times fraction numerator square root of x squared plus 7 end root plus 4 over denominator square root of x squared plus 7 end root plus 4 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator open parentheses x squared minus 9 close parentheses open parentheses square root of x squared plus 7 end root plus 4 close parentheses over denominator x squared plus 7 minus 16 end fraction end cell row blank equals cell limit as x rightwards arrow 3 of fraction numerator down diagonal strike open parentheses x squared minus 9 close parentheses end strike open parentheses square root of x squared plus 7 end root plus 4 close parentheses over denominator down diagonal strike x squared minus 9 end strike end fraction end cell row blank equals cell limit as x rightwards arrow 3 of square root of x squared plus 7 end root plus 4 end cell end table end style

Kemudian substitusi limit yang diperoleh dengan begin mathsize 14px style x equals 3 end style seperti berikut:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of square root of x squared plus 7 end root plus 4 end cell equals cell square root of 3 squared plus 7 end root plus 4 end cell row blank equals cell square root of 9 plus 7 end root plus 4 end cell row blank equals cell square root of 16 plus 4 end cell row blank equals cell 4 plus 4 end cell row blank equals 8 end table end style

Nilai dari begin mathsize 14px style limit as x rightwards arrow 3 of fraction numerator x squared minus 9 over denominator square root of x squared plus 7 end root minus 4 end fraction end style adalah begin mathsize 14px style 8 end style.

Jadi, jawaban yang tepat adalah D.

333

4.3 (18 rating)

Cantika Reika Viana

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