Pertanyaan

Nilai dari x → 0 lim x 2 + x − 2 − x adalah ....

Nilai dari $x \to 0 lim \frac{2 + x - 2 - x}{x}$ adalah ....

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Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari $limit as straight x rightwards arrow 0 of space fraction numerator square root of 2 plus square root of straight x end root minus square root of 2 minus square root of straight x end root over denominator square root of straight x end fraction$ adalah 1 half square root of 2

Pembahasan

Jadi, nilai dari adalah .

$limit as straight x rightwards arrow 0 of space fraction numerator square root of 2 plus square root of straight x end root minus square root of 2 minus square root of straight x end root over denominator square root of straight x end fraction equals limit as straight x rightwards arrow 0 of space fraction numerator square root of 2 plus square root of straight x end root minus square root of 2 minus square root of straight x end root over denominator square root of straight x end fraction times fraction numerator square root of 2 plus square root of straight x end root plus square root of 2 minus square root of straight x end root over denominator square root of 2 plus square root of straight x end root plus square root of 2 minus square root of straight x end root end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as straight x rightwards arrow 0 of space fraction numerator open parentheses 2 plus square root of straight x minus 2 plus square root of straight x close parentheses over denominator square root of straight x times open parentheses square root of 2 plus square root of straight x end root plus square root of 2 minus square root of straight x end root close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as straight x rightwards arrow 0 of space fraction numerator 2 square root of straight x over denominator square root of straight x times open parentheses square root of 2 plus square root of straight x end root plus square root of 2 minus square root of straight x end root close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as straight x rightwards arrow 0 of space fraction numerator 2 over denominator open parentheses square root of 2 plus square root of straight x end root plus square root of 2 minus square root of straight x end root close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 over denominator open parentheses square root of 2 plus square root of 0 end root plus square root of 2 minus square root of 0 end root close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 over denominator open parentheses square root of 2 plus 0 end root plus square root of 2 minus 0 end root close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 over denominator open parentheses square root of 2 plus square root of 2 close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 over denominator 2 square root of 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 1 over denominator square root of 2 end fraction times fraction numerator square root of 2 over denominator square root of 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half square root of 2$

Jadi, nilai dari $limit as straight x rightwards arrow 0 of space fraction numerator square root of 2 plus square root of straight x end root minus square root of 2 minus square root of straight x end root over denominator square root of straight x end fraction$ adalah 1 half square root of 2 .