Pertanyaan

Tentukan nilai dari x → ∞ lim ( x + 2 − x + 1 ) = ....

Tentukan nilai dari $x \to \infty lim (x + 2 - x + 1) = ....$

N. Puspita

Master Teacher

Jawaban terverifikasi

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nilai dari .

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

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

Limit tak hingga Jika diketahui dan , maka terlebih dahulu fungsi tersebut dikalikan dengansekawannya. Dari hasil diatas diperoleh Pembilang memiliki derajat Penyebut memiliki derajat Diperoleh Jadi,nilai dari .

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

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 memiliki derajat
Penyebut memiliki derajat

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 .

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