Tentukan nilai limit berikut. a. limx→6 2x−1236−3x

Pertanyaan

Tentukan nilai limit berikut.

a. $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 6 of space fraction numerator 3 square root of 6 minus 3 square root of x over denominator 2 x minus 12 end fraction end cell end table$

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai limit tersebut adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative fraction numerator square root of 6 over denominator 8 end fraction end cell end table$ .

Pembahasan

Untuk menentukan nilai limit tersebut apabila menggunakan metode substitusi akan diperoleh nilai $\frac00$ seperti berikut:

Oleh sebab itu, gunakan metode mengalikan akar sekawan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 6 of space fraction numerator 3 square root of 6 minus 3 square root of x over denominator 2 x minus 12 end fraction end cell equals cell limit as x rightwards arrow 6 of space fraction numerator 3 square root of 6 minus 3 square root of x over denominator 2 x minus 12 end fraction cross times fraction numerator 3 square root of 6 plus 3 square root of x over denominator 3 square root of 6 plus 3 square root of x end fraction end cell row blank equals cell limit as x rightwards arrow 6 of space fraction numerator 54 minus 9 x over denominator left parenthesis 2 x minus 12 right parenthesis left parenthesis 3 square root of 6 plus 3 square root of x right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 6 of space fraction numerator negative 9 left parenthesis x minus 6 right parenthesis over denominator 2 left parenthesis x minus 6 right parenthesis left parenthesis 3 square root of 6 plus 3 square root of x right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 6 of space fraction numerator negative 9 over denominator 2 left parenthesis 3 square root of 6 plus 3 square root of x right parenthesis end fraction end cell row blank equals cell fraction numerator negative 9 over denominator 2 left parenthesis 3 square root of 6 plus 3 square root of 6 right parenthesis end fraction end cell row blank equals cell fraction numerator negative 9 over denominator 12 square root of 6 end fraction end cell row blank equals cell negative fraction numerator 3 over denominator 4 square root of 6 end fraction cross times fraction numerator square root of 6 over denominator square root of 6 end fraction end cell row blank equals cell negative 3 over 24 square root of 6 end cell row blank equals cell negative fraction numerator square root of 6 over denominator 8 end fraction end cell end table$

Dengan demikian, nilai limit tersebut adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative fraction numerator square root of 6 over denominator 8 end fraction end cell end table$ .