Pertanyaan

Selesaikan soal-soal berikut! x → ∞ lim ( x + a − x )

Selesaikan soal-soal berikut!

$x \to \infty lim (x + a - x)$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari adalah 0.

nilai dari limit as x rightwards arrow infinity of open parentheses square root of x plus a end root minus square root of x close parentheses

adalah 0.

Pembahasan

Kalikan bentuk sekawan dari akar tersebut, kemudian bagilah dengan variabel pangkat tertinggi: Dengan demikian nilai dari adalah 0.

Kalikan bentuk sekawan dari akar tersebut, kemudian bagilah dengan variabel pangkat tertinggi:

$begin mathsize 12px style 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 a end root minus square root of x close parentheses end cell equals cell limit as x rightwards arrow infinity of open parentheses square root of x plus a end root minus square root of x close parentheses cross times fraction numerator square root of x plus a end root plus square root of x over denominator square root of x plus a end root plus square root of x end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator x plus a minus x over denominator square root of x plus a end root plus square root of x end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator a over denominator square root of x plus a end root plus square root of x end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style a over x to the power of begin display style 1 half end style end exponent end style over denominator square root of begin display style x over x end style plus begin display style a over x end style end root plus square root of begin display style x over x end style end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style a over x to the power of begin display style 1 half end style end exponent end style over denominator square root of begin display style 1 plus a over x 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 square root of 1 plus 0 end root plus square root of 1 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 end style$

Dengan demikian nilai dari limit as x rightwards arrow infinity of open parentheses square root of x plus a end root minus square root of x close parentheses adalah 0.

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