Pertanyaan

Jika x → ∞ lim x g ( x ) = 1 , maka nilai x → ∞ lim 1 − x − 1 g ( x ) adalah ....

Jika $x \to \infty lim \frac{g ( x )}{x} = 1,$ maka nilai $x \to \infty lim \frac{g ( x )}{1 - x - 1}$ adalah ....

A. Allamah

Master Teacher

Mahasiswa/Alumni Universitas Brawijaya

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Pembahasan

Limit menuju tak hingga Jadi,nilai adalah . Jadi, tidak ada jawaban yang tepat dipilihan ganda tersebut.

Limit menuju tak hingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator g left parenthesis x right parenthesis over denominator square root of 1 minus x end root minus 1 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator g left parenthesis x right parenthesis over denominator square root of 1 minus x end root minus 1 end fraction times fraction numerator square root of 1 minus x end root plus 1 over denominator square root of 1 minus x end root plus 1 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator g left parenthesis x right parenthesis open parentheses square root of 1 minus x end root plus 1 close parentheses over denominator 1 minus x minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator g left parenthesis x right parenthesis open parentheses square root of 1 minus x end root plus 1 close parentheses over denominator negative x end fraction end cell row blank equals cell negative limit as x rightwards arrow infinity of fraction numerator g left parenthesis x right parenthesis over denominator x end fraction times limit as x rightwards arrow infinity of open parentheses square root of 1 minus x end root plus 1 close parentheses end cell row blank equals cell negative 1 times infinity end cell row blank equals cell negative infinity end cell end table$

Jadi, nilai $limit as x rightwards arrow infinity of fraction numerator g left parenthesis x right parenthesis over denominator square root of 1 minus x end root minus 1 end fraction$ adalah negative sign infinity .

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