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 0 over 0 seperti berikut:

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 fraction numerator 3 square root of 6 minus 3 square root of 6 over denominator 2 open parentheses 6 close parentheses minus 12 end fraction end cell row blank equals cell fraction numerator 3 square root of 6 minus 3 square root of 6 over denominator 12 minus 12 end fraction end cell row blank equals cell 0 over 0 end cell end table 

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

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