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x→∞lim​ (x+7​−x−2​)=.....

Pertanyaan

limit as x rightwards arrow infinity of space open parentheses square root of x plus 7 end root minus square root of x minus 2 end root close parentheses equals.....

  1. negative infinity

  2. 0

  3. 5

  4. 9

  5. infinity

T. Prita

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Nilai limit tak hingga dari suatu fungsi bentuk akar dapat ditentukan sebagai berikut.

begin mathsize 12px style limit as x rightwards arrow infinity of open parentheses square root of a x plus b end root minus square root of c x plus d end root close parentheses equals open curly brackets table row cell infinity comma space text untuk end text space a greater than c end cell row cell table attributes columnalign left end attributes row cell 0 comma space text untuk end text space a equals c end cell row cell negative infinity comma space text untuk end text space a less than c end cell end table end cell end table close end style

Diketahui: limit as x rightwards arrow infinity of space open parentheses square root of x plus 7 end root minus square root of x minus 2 end root close parentheses

Bentuk soal limit di atas memiliki nilai a equals c equals 1, sehingga nilai limit as x rightwards arrow infinity of space open parentheses square root of x plus 7 end root minus square root of x minus 2 end root close parentheses equals 0.

 

Atau dapat menggunakan perkalian akar sekawan dengan konsep:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space k over x to the power of n end cell equals 0 end table, dengan k equals text konstanta end text

untuk menentukan nilai limit tersebut sebagai berikut.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space open parentheses square root of x plus 7 end root minus square root of x minus 2 end root close parentheses end cell equals cell limit as x rightwards arrow infinity of space open parentheses square root of x plus 7 end root minus square root of x minus 2 end root close parentheses times fraction numerator square root of x plus 7 end root plus square root of x minus 2 end root over denominator square root of x plus 7 end root plus square root of x minus 2 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator open parentheses x plus 7 close parentheses minus open parentheses x minus 2 close parentheses over denominator square root of x plus 7 end root plus square root of x minus 2 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator x plus 7 minus x plus 2 over denominator square root of x plus 7 end root plus square root of x minus 2 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator 9 over denominator square root of x plus 7 end root plus square root of x minus 2 end root end fraction end cell end table end style

Bagi pembilang dan penyebut dengan pangkat tertinggi yaitu square root of x.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator 9 over denominator square root of x plus 7 end root plus square root of x minus 2 end root end fraction end cell equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style fraction numerator 9 over denominator square root of x end fraction end style over denominator square root of begin display style x over x end style plus begin display style 7 over x end style end root plus square root of begin display style x over x end style minus begin display style 2 over x end style end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style fraction numerator 9 over denominator square root of x end fraction end style over denominator square root of begin display style 1 plus 7 over x end style end root plus square root of begin display style 1 minus 2 over x end style end root end fraction end cell row blank equals cell fraction numerator begin display style 0 end style over denominator square root of begin display style 1 plus 0 end style end root plus square root of begin display style 1 minus 0 end style end root end fraction end cell row blank equals cell fraction numerator begin display style 0 end style over denominator square root of begin display style 1 end style end root plus square root of begin display style 1 end style end root end fraction end cell row blank equals cell fraction numerator 0 over denominator 1 plus 1 end fraction end cell row blank equals cell 0 over 2 end cell row blank equals 0 end table

Oleh karena itu, jawaban yang benar adalah B.

101

4.2 (7 rating)

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