Pertanyaan

Nilai dari x → 1 lim ( x − 1 3 − x 2 − 1 6 ) adalah ....

Nilai dari $x \to 1 lim (\frac{3}{x - 1} - \frac{6}{x ^{2} - 1})$ adalah ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Dapat diperhatikan bahwa . Kemudian, perhatikan perhitungan berikut ini! Dengan demikian,Nilai dari adalah . Jadi, jawaban yang tepat adalah D.

Dapat diperhatikan bahwa . Kemudian, perhatikan perhitungan berikut ini!

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator 3 over denominator x minus 1 end fraction minus fraction numerator 6 over denominator x squared minus 1 end fraction close parentheses 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 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator 3 open parentheses x plus 1 close parentheses over denominator open parentheses x minus 1 close parentheses open parentheses x plus 1 close parentheses end fraction minus fraction numerator 6 over denominator x squared minus 1 end fraction close parentheses 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 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator 3 open parentheses x plus 1 close parentheses over denominator open parentheses x minus 1 close parentheses open parentheses x plus 1 close parentheses end fraction minus fraction numerator 6 over denominator left parenthesis x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis end fraction close parentheses 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 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator 3 open parentheses x plus 1 close parentheses minus 6 over denominator open parentheses x minus 1 close parentheses open parentheses x plus 1 close parentheses end fraction close parentheses 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 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator 3 x plus 3 minus 6 over denominator open parentheses x minus 1 close parentheses open parentheses x plus 1 close parentheses end fraction close parentheses 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 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator 3 x minus 3 over denominator open parentheses x minus 1 close parentheses open parentheses x plus 1 close parentheses end fraction close parentheses 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 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator 3 up diagonal strike open parentheses x minus 1 close parentheses end strike over denominator up diagonal strike open parentheses x minus 1 close parentheses end strike open parentheses x plus 1 close parentheses end fraction close parentheses 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 1 of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank invisible function application end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator 3 over denominator open parentheses x plus 1 close parentheses end fraction close parentheses 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 3 over denominator 1 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 cell 3 over 2 end cell end table end style$

Dengan demikian, Nilai dari $begin mathsize 14px style limit as x rightwards arrow 1 of invisible function application open parentheses fraction numerator 3 over denominator x minus 1 end fraction minus fraction numerator 6 over denominator x squared minus 1 end fraction close parentheses end style$ adalah .

Jadi, jawaban yang tepat adalah D.