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Tentukan nilai dari x → ∞ lim ​ 1 + x 2 − 2 x ​ x ​ .

Tentukan nilai dari .

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N. Puspita

Master Teacher

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nilai dari .

 nilai dari limit as x rightwards arrow infinity of 1 plus fraction numerator x over denominator square root of x squared minus 2 x end root end fraction equals 2.

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Limit tak hingga Jadi,nilai dari .

Limit tak hingga

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

Jadi, nilai dari limit as x rightwards arrow infinity of 1 plus fraction numerator x over denominator square root of x squared minus 2 x end root end fraction equals 2.

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