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Tentukan nilai dari

Pertanyaan

Tentukan nilai dari limit as x rightwards arrow infinity of open parentheses square root of x plus 2 end root minus square root of x plus 1 end root close parentheses equals....

Pembahasan Soal:

Limit tak hingga

Jika diketahui limit as x rightwards arrow infinity of open parentheses square root of x plus 2 end root minus square root of x plus 1 end root close parentheses dan

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of x plus 2 end root minus square root of x plus 1 end root close parentheses end cell equals cell limit as x rightwards arrow infinity of open parentheses square root of infinity plus 2 end root minus square root of infinity plus 1 end root close parentheses end cell row blank equals infinity end table,

maka terlebih dahulu fungsi tersebut dikalikan dengan sekawannya.

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses square root of x plus 2 end root minus square root of x plus 1 end root close parentheses times fraction numerator open parentheses square root of x plus 2 end root plus square root of x plus 1 end root close parentheses over denominator open parentheses square root of x plus 2 end root plus square root of x plus 1 end root close parentheses end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses x plus 2 minus x minus 1 close parentheses over denominator open parentheses square root of x plus 2 end root plus square root of x plus 1 end root close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 1 over denominator open parentheses square root of x plus 2 end root plus square root of x plus 1 end root close parentheses end fraction end cell end table

Dari hasil diatas diperoleh

  • Pembilang 1 memiliki derajat 0
  • Penyebut table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of x plus 2 end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of x plus 1 end root end cell end table memiliki derajat 1 half

Diperoleh

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

Jadi, nilai dari limit as x rightwards arrow infinity of open parentheses square root of x plus 2 end root minus square root of x plus 1 end root close parentheses equals 0.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 01 Agustus 2021

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