x→∞lim​ (3x−5​−2x+7​)=.....

Pertanyaan

limit as x rightwards arrow infinity of space open parentheses square root of 3 x minus 5 end root minus square root of 2 x plus 7 end root close parentheses equals.....

  1. negative infinity

  2. negative 12

  3. 0

  4. 1

  5. infinity

T. Prita

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

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 3 x minus 5 end root minus square root of 2 x plus 7 end root close parentheses

Bentuk soal limit di atas memiliki nilai a equals 3, c equals 2 dalam hal ini a greater than c, sehingga nilai limit as x rightwards arrow infinity of space open parentheses square root of 3 x minus 5 end root minus square root of 2 x plus 7 end root close parentheses equals infinity.

 

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 3 x minus 5 end root minus square root of 2 x plus 7 end root close parentheses end cell equals cell limit as x rightwards arrow infinity of space open parentheses square root of 3 x minus 5 end root minus square root of 2 x plus 7 end root close parentheses times fraction numerator square root of 3 x minus 5 end root plus square root of 2 x plus 7 end root over denominator square root of 3 x minus 5 end root plus square root of 2 x plus 7 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator 3 x minus 5 minus open parentheses 2 x plus 7 close parentheses over denominator square root of 3 x minus 5 end root plus square root of 2 x plus 7 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator 3 x minus 5 minus 2 x minus 7 over denominator square root of 3 x minus 5 end root plus square root of 2 x plus 7 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator x minus 12 over denominator square root of 3 x minus 5 end root plus square root of 2 x plus 7 end root end fraction end cell end table end style

Bagi pembilang dan penyebut dengan pangkat tertinggi yaitu x text  atau end text space square root of x squared end root. Untuk pembilang di bagi dengan x sedangkan penyebut dibagi dengan square root of x squared end root

table attributes columnalign right center left columnspacing 0px end attributes row cell size 12px lim with size 12px x size 12px rightwards arrow size 12px infinity below size 12px space fraction numerator size 12px x size 12px minus size 12px 12 over denominator square root of size 12px 3 size 12px x size 12px minus size 12px 5 end root size 12px plus square root of size 12px 2 size 12px x size 12px plus size 12px 7 end root end fraction end cell size 12px equals cell size 12px lim with size 12px x size 12px rightwards arrow size 12px infinity below size 12px space fraction numerator begin display style size 12px x over size 12px x end style size 12px minus begin display style size 12px 12 over size 12px x end style over denominator square root of begin display style fraction numerator size 12px 3 size 12px x over denominator size 12px x to the power of size 12px 2 end fraction end style size 12px minus begin display style size 12px 5 over size 12px x end style end root size 12px plus square root of begin display style fraction numerator size 12px 2 size 12px x over denominator size 12px x to the power of size 12px 2 end fraction end style size 12px plus begin display style size 12px 7 over size 12px x end style end root end fraction end cell row blank size 12px equals cell size 12px lim with size 12px x size 12px rightwards arrow size 12px infinity below size 12px space fraction numerator begin mathsize 12px display style 1 minus 12 over x end style over denominator square root of begin mathsize 12px display style fraction numerator begin display style 3 end style over denominator x end fraction minus 5 over x end style end root size 12px plus square root of begin mathsize 12px display style fraction numerator begin display style 2 end style over denominator x end fraction plus 7 over x end style end root end fraction end cell row blank size 12px equals cell fraction numerator size 12px 1 size 12px minus size 12px 0 over denominator square root of size 12px 0 size 12px minus size 12px 0 end root size 12px plus square root of size 12px 0 size 12px plus size 12px 0 end root end fraction end cell row blank size 12px equals cell fraction numerator size 12px 1 over denominator square root of size 12px 0 size 12px plus square root of size 12px 0 end fraction end cell row blank size 12px equals cell size 12px 1 over size 12px 0 end cell row blank size 12px equals size 12px infinity end table

Oleh karena itu, jawaban yang benar adalah E.

144

5.0 (6 rating)

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