Pertanyaan

Nilai dari b b lo g x → ∞ lim − 100 b x n − bx − 100 bx n + bx adalah ...

Nilai dari $b^{b} lo g x \to \infty lim \frac{- 100 bx ^{n} + bx}{- \frac{b}{100} x ^{n} - bx}$ adalah ...

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P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

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$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight b end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank presuperscript straight b end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank log end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 100 bx to the power of straight n plus bx over denominator negative begin display style straight b over 100 end style straight x to the power of straight n minus bx end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 000 end table end style$ .

Pembahasan

Soal tersebut dapat diselesaikan dengan cara berikut. Dengan demikian, .

Soal tersebut dapat diselesaikan dengan cara berikut.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight b space log presuperscript straight b limit as straight x rightwards arrow infinity of fraction numerator negative 100 bx to the power of straight n plus bx over denominator negative begin display style straight b over 100 end style straight x to the power of straight n minus bx end fraction end cell equals cell limit as straight x rightwards arrow infinity of fraction numerator negative 100 bx to the power of straight n plus bx over denominator negative begin display style straight b over 100 end style straight x to the power of straight n minus bx end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of open parentheses negative 100 straight b plus begin display style bx over straight x to the power of straight n end style close parentheses to the power of straight x to the power of straight n end exponent over open parentheses negative begin display style straight b over 100 end style minus bx over straight x to the power of straight n close parentheses to the power of straight x to the power of straight n end exponent end cell row blank equals cell fraction numerator open parentheses negative 100 straight b plus 0 close parentheses over denominator open parentheses negative begin display style straight b over 100 end style minus 0 close parentheses end fraction end cell row blank equals cell 10.000 end cell end table end style$

Dengan demikian, $begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight b end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank presuperscript straight b end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank log end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 100 bx to the power of straight n plus bx over denominator negative begin display style straight b over 100 end style straight x to the power of straight n minus bx end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 000 end table end style$ .