Pertanyaan

x → ∞ lim x + 2 − x + 4 = ....

$x \to \infty lim x + 2 - x + 4 =$ ....

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Klaim

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

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Jawaban

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limit as x rightwards arrow infinity of square root of x plus 2 end root minus square root of x plus 4 end root equals

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$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of square root of x plus 2 end root minus square root of x plus 4 end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of x plus 2 end root minus square root of x plus 4 end root cross times fraction numerator square root of x plus 2 end root plus square root of x plus 4 end root over denominator square root of x plus 2 end root plus square root of x plus 4 end root end fraction end cell row blank equals cell stack l i m with x rightwards arrow infinity below fraction numerator open parentheses x plus 2 close parentheses minus open parentheses x plus 4 close parentheses over denominator square root of x plus 2 end root plus square root of x plus 4 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator negative 2 over denominator square root of x plus 2 end root plus square root of x plus 4 end root end fraction cross times fraction numerator square root of x over denominator square root of x end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator negative 2 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 2 over x end style end root plus square root of begin display style x over x end style plus begin display style 4 over x end style end root end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator negative 2 over denominator infinity end fraction end style over denominator square root of 1 plus begin display style 2 over infinity end style end root plus square root of 1 plus begin display style 4 over infinity end style 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 cell 0 over 2 end cell row blank equals 0 end table$

Jadi, limit as x rightwards arrow infinity of square root of x plus 2 end root minus square root of x plus 4 end root equals 0.

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