Pertanyaan

x → 3 lim 2 x 2 + 3 − 4 3 9 − x 2 = ...

$x \to 3 lim \frac{9 - x ^{2}}{2 x ^{2} + 3 - 4 3} = ...$

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Klaim

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style space space space space limit as x rightwards arrow 3 of fraction numerator 9 minus x squared over denominator 2 square root of x squared plus 3 end root minus 4 square root of 3 end fraction equals limit as x rightwards arrow 3 of fraction numerator 9 minus x squared over denominator 2 square root of x squared plus 3 end root minus 4 square root of 3 end fraction cross times fraction numerator 2 square root of x squared plus 3 end root plus 4 square root of 3 over denominator 2 square root of x squared plus 3 end root plus 4 square root of 3 end fraction equals limit as x rightwards arrow 3 of fraction numerator open parentheses 9 minus x squared close parentheses open parentheses 2 square root of x squared plus 3 end root plus 4 square root of 3 close parentheses over denominator 4 open parentheses x squared plus 3 close parentheses minus 16 open parentheses 3 close parentheses end fraction equals limit as x rightwards arrow 3 of fraction numerator open parentheses 9 minus x squared close parentheses open parentheses 2 square root of x squared plus 3 end root plus 4 square root of 3 close parentheses over denominator 4 x squared minus 36 end fraction equals limit as x rightwards arrow 3 of fraction numerator down diagonal strike open parentheses 9 minus x squared close parentheses end strike open parentheses 2 square root of x squared plus 3 end root plus 4 square root of 3 close parentheses over denominator negative 4 down diagonal strike open parentheses 9 minus x squared close parentheses end strike end fraction equals limit as x rightwards arrow 3 of fraction numerator open parentheses 2 square root of x squared plus 3 end root plus 4 square root of 3 close parentheses over denominator negative 4 end fraction equals fraction numerator open parentheses 2 square root of 3 squared plus 3 end root plus 4 square root of 3 close parentheses over denominator negative 4 end fraction equals fraction numerator open parentheses 2 square root of 12 plus 4 square root of 3 close parentheses over denominator negative 4 end fraction equals fraction numerator open parentheses 4 square root of 3 plus 4 square root of 3 close parentheses over denominator negative 4 end fraction equals negative 2 square root of 3 end style$

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