Pertanyaan

Tentukannilai limit berikut! x → 4 lim − 2 x − 4 − 2 x − 2

Tentukan nilai limit berikut!

$x \to 4 lim - \frac{x - 2}{2 x - 4 - 2}$

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Habis dalam

Klaim

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of minus fraction numerator square root of x minus 2 over denominator square root of 2 x minus 4 end root minus 2 end fraction end cell equals cell limit as x rightwards arrow 4 of open parentheses negative fraction numerator square root of x minus 2 over denominator square root of 2 x minus 4 end root minus 2 end fraction close parentheses times open parentheses fraction numerator square root of 2 x minus 4 end root plus 2 over denominator square root of 2 x minus 4 end root plus 2 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow 4 of minus fraction numerator open parentheses square root of x minus 2 close parentheses open parentheses square root of 2 x minus 4 end root plus 2 close parentheses over denominator open parentheses 2 x minus 4 close parentheses minus open parentheses 4 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 4 of minus fraction numerator open parentheses square root of x minus 2 close parentheses open parentheses square root of 2 x minus 4 end root plus 2 close parentheses over denominator 2 x minus 8 end fraction space end cell row blank equals cell limit as x rightwards arrow 4 of minus fraction numerator open parentheses square root of x minus 2 close parentheses open parentheses square root of 2 x minus 4 end root plus 2 close parentheses over denominator 2 open parentheses x minus 4 close parentheses end fraction space end cell row blank equals cell limit as x rightwards arrow 4 of minus fraction numerator open parentheses square root of x minus 2 close parentheses open parentheses square root of 2 x minus 4 end root plus 2 close parentheses over denominator 2 open parentheses square root of x minus 2 close parentheses open parentheses square root of x plus 2 close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow 4 of minus fraction numerator square root of 2 x minus 4 end root plus 2 over denominator 2 open parentheses square root of x plus 2 close parentheses end fraction end cell row blank equals cell negative fraction numerator square root of 2 open parentheses 4 close parentheses minus 4 end root plus 2 over denominator 2 left parenthesis square root of 4 plus 2 right parenthesis end fraction end cell row blank equals cell negative fraction numerator square root of 4 plus 2 over denominator 2 open parentheses 4 close parentheses end fraction end cell row blank equals cell negative 4 over 8 end cell row blank equals cell negative 1 half end cell end table end style$

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