Pertanyaan

Hasil dari adalah ...

Hasil dari $limit as x rightwards arrow 4 of invisible function application fraction numerator sin invisible function application open parentheses x squared minus 9 x plus 20 close parentheses over denominator tan invisible function application open parentheses x squared minus 5 x plus 4 close parentheses end fraction$ adalah ...

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Misalkan dan , maka limit pada soal dapat dihitung sebagai berikut. Diketahui dan .Karena Artinya, dan . Dengan demikian, didapat perhitungan berikut. Dengan demikian,hasil dari adalah . Jadi, jawaban yang tepat adalah D.

Misalkan x squared minus 9 x plus 20 equals a dan x squared minus 5 x plus 4 equals b , maka limit pada soal dapat dihitung sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 4 of invisible function application fraction numerator sin invisible function application open parentheses x squared minus 9 x plus 20 close parentheses over denominator tan invisible function application open parentheses x squared minus 5 x plus 4 close parentheses end fraction end cell equals cell limit as x rightwards arrow 4 of invisible function application fraction numerator sin invisible function application a over denominator tan invisible function application b end fraction end cell row blank equals cell limit as x rightwards arrow 4 of invisible function application fraction numerator sin invisible function application a over denominator tan invisible function application b end fraction times a over a times b over b end cell row blank equals cell limit as x rightwards arrow 4 of invisible function application fraction numerator sin invisible function application a over denominator a end fraction times fraction numerator b over denominator tan invisible function application b end fraction times a over b end cell row blank equals cell limit as x rightwards arrow 4 of invisible function application fraction numerator sin invisible function application a over denominator a end fraction times limit as x rightwards arrow 4 of invisible function application fraction numerator b over denominator tan invisible function application b end fraction times limit as x rightwards arrow 4 of invisible function application a over b end cell end table$

Diketahui a equals x squared minus 9 x plus 20 equals left parenthesis x minus 5 right parenthesis left parenthesis x minus 4 right parenthesis dan b equals x squared minus 5 x plus 4 equals left parenthesis x minus 1 right parenthesis left parenthesis x minus 4 right parenthesis . Karena Artinya, a rightwards arrow 0 dan b rightwards arrow 0 . Dengan demikian, didapat perhitungan berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 4 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 fraction numerator sin invisible function application a over denominator a 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 limit as x rightwards arrow 4 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 fraction numerator b over denominator tan invisible function application b 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 limit as x rightwards arrow 4 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 a over b 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 a rightwards arrow 0 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 fraction numerator sin invisible function application a over denominator a end fraction times limit as a rightwards arrow 0 of invisible function application fraction numerator b over denominator tan invisible function application b 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 limit as x rightwards arrow 4 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 a over b 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 1 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 1 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 limit as x rightwards arrow 4 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 fraction numerator left parenthesis x minus 5 right parenthesis left parenthesis x minus 4 right parenthesis over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 4 right parenthesis 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 1 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 1 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 limit as x rightwards arrow 4 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 fraction numerator left parenthesis x minus 5 right parenthesis up diagonal strike left parenthesis x minus 4 right parenthesis end strike over denominator left parenthesis x minus 1 right parenthesis up diagonal strike left parenthesis x minus 4 right parenthesis end strike 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 1 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 1 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 limit as x rightwards arrow 4 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 fraction numerator left parenthesis x minus 5 right parenthesis over denominator left parenthesis x minus 1 right parenthesis 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 1 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 1 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 third 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 third end cell end table$

Dengan demikian, hasil dari $limit as x rightwards arrow 4 of invisible function application fraction numerator sin invisible function application open parentheses x squared minus 9 x plus 20 close parentheses over denominator tan invisible function application open parentheses x squared minus 5 x plus 4 close parentheses end fraction$ adalah negative 1 third .

Jadi, jawaban yang tepat adalah D.