Pertanyaan

x → ∞ lim − 4 + ln x + 1 7 + ln x 9 8 + ln x + 1 9 + ln x 7 = ....

$x \to \infty lim \frac{8 + ln ^{x + 1} 9 + ln ^{x} 7}{- 4 + ln ^{x + 1} 7 + ln ^{x} 9} =$ .... $\;\;$

$begin mathsize 14px style fraction numerator 1 over denominator blank ln squared 7 end fraction end style$
$begin mathsize 14px style fraction numerator 1 over denominator blank ln squared 9 end fraction end style$

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

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$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as 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 8 plus ln to the power of x plus 1 end exponent 9 plus ln to the power of x 7 over denominator negative 4 plus ln to the power of x plus 1 end exponent 7 plus ln to the power of x 9 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 cell limit as 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 8 plus left parenthesis ln to the power of x 9 right parenthesis left parenthesis ln space 9 right parenthesis plus ln to the power of x 7 over denominator negative 4 plus left parenthesis ln to the power of x 7 right parenthesis left parenthesis ln space 7 right parenthesis plus ln to the power of x 9 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 cell limit as 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 8 plus left parenthesis ln to the power of x 9 right parenthesis left parenthesis ln space 9 right parenthesis plus ln to the power of x 7 over denominator negative 4 plus left parenthesis ln to the power of x 7 right parenthesis left parenthesis ln space 7 right parenthesis plus ln to the power of x 9 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator begin display style fraction numerator 1 over denominator ln to the power of x 9 end fraction end style over denominator begin display style fraction numerator 1 over denominator ln to the power of x 9 end fraction end style 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 cell limit as 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 begin display style fraction numerator 8 over denominator ln to the power of x 9 end fraction plus fraction numerator open parentheses ln to the power of x 9 close parentheses open parentheses ln space 9 close parentheses over denominator ln to the power of x 9 end fraction plus fraction numerator ln to the power of x 7 over denominator ln to the power of x 9 end fraction end style over denominator begin display style fraction numerator negative 4 over denominator ln to the power of x 9 end fraction plus fraction numerator open parentheses ln to the power of x 7 close parentheses open parentheses ln space 7 close parentheses over denominator ln to the power of x 9 end fraction plus fraction numerator ln to the power of x 9 over denominator ln to the power of x 9 end fraction end style 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 cell limit as 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 begin display style fraction numerator 8 over denominator ln to the power of x 9 end fraction plus ln space 9 plus open parentheses fraction numerator ln space 7 over denominator ln space 9 end fraction close parentheses to the power of x end style over denominator begin display style fraction numerator negative 4 over denominator ln to the power of x 9 end fraction plus ln space 7 space open parentheses fraction numerator ln space 7 over denominator ln space 9 end fraction close parentheses to the power of x plus 1 end style 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 cell fraction numerator begin display style limit as x rightwards arrow infinity of fraction numerator 8 over denominator ln to the power of x 9 end fraction plus limit as x rightwards arrow infinity of ln space 9 plus limit as x rightwards arrow infinity of open parentheses fraction numerator ln space 7 over denominator ln space 9 end fraction close parentheses to the power of x end style over denominator begin display style limit as x rightwards arrow infinity of fraction numerator negative 4 over denominator ln to the power of x 9 end fraction plus limit as x rightwards arrow infinity of ln space 7 space open parentheses fraction numerator ln space 7 over denominator ln space 9 end fraction close parentheses to the power of x plus limit as x rightwards arrow infinity of 1 end style 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 cell fraction numerator 0 plus ln space 9 plus 0 over denominator 0 plus 0 plus 1 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 ln 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 9 end table end style$

Dengan demikian, $begin mathsize 14px style limit as straight x rightwards arrow straight infinity of space fraction numerator 8 plus ln to the power of straight x plus 1 end exponent 9 plus ln to the power of straight x space 7 over denominator negative 4 plus ln to the power of straight x plus 1 end exponent 7 plus ln to the power of straight x 9 end fraction equals ln space 9 end style$

Jadi, jawaban yang tepat adalah E.

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