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Jika . Berapakah nilai ?

Pertanyaan

Jika limit as x rightwards arrow 3 of fraction numerator x squared plus 2 a x plus b over denominator x minus 3 end fraction equals 8. Berapakah nilai a times b?

  1. 15

  2. negative 15

  3. 132

  4. negative 132

  5. 12

Pembahasan Soal:

Kita gunakan metode substitusi sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x squared plus 2 a x plus b over denominator x minus 3 end fraction end cell equals 8 row cell fraction numerator 3 squared plus 2 times 3 times a plus b over denominator 3 minus 3 end fraction end cell equals 8 row cell fraction numerator 9 plus 6 a plus b over denominator 0 end fraction end cell equals 8 row cell 9 plus 6 a plus b end cell equals 0 row cell 6 a plus b end cell equals cell negative 9 end cell end table

Kemudian gunakan aturan L'Hospital yaitu dengan mencari turunan dari pembilang dan penyebut.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 3 of fraction numerator x squared plus 2 a x plus b over denominator x minus 3 end fraction end cell equals 8 row cell limit as x rightwards arrow 3 of fraction numerator 2 times x to the power of 2 minus 1 end exponent plus 2 times 1 times a times x to the power of 1 minus 1 end exponent plus b over denominator 1 times 1 times x to the power of 1 minus 1 end exponent minus 3 end fraction end cell equals 8 row cell limit as x rightwards arrow 3 of fraction numerator 2 x plus 2 a over denominator 1 end fraction end cell equals 8 row cell fraction numerator 2 times 3 plus 2 a over denominator 1 end fraction end cell equals 8 row cell 6 plus 2 a end cell equals 8 row cell 2 a end cell equals cell 8 minus 6 end cell row cell 2 a end cell equals 2 row a equals 1 end table

Lalu kita substitusikan nilai a ke persamaan 6 a plus b equals negative 9.

table attributes columnalign right center left columnspacing 0px end attributes row cell 6 a plus b end cell equals cell negative 9 end cell row cell 6 times 1 plus b end cell equals cell negative 9 end cell row b equals cell negative 9 minus 6 end cell row blank equals cell negative 15 end cell end table

Sehingga nilai a times b equals 1 times negative 15 equals negative 15.

Oleh karena itu, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 28 April 2021

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