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Tentukan nilai  dengan menunjukkan pendekatan nilai dan proses pergantian fungsi dengan faktorisasi.

Pertanyaan

Tentukan nilai begin mathsize 14px style stack L i m with x rightwards arrow 1 below fraction numerator open parentheses 3 x minus 1 close parentheses cubed minus open parentheses x plus 1 close parentheses cubed over denominator x cubed minus 1 end fraction end style dengan menunjukkan pendekatan nilai dan proses pergantian fungsi dengan faktorisasi.

  1. ....space space space 

  2. ....space space space 

Pembahasan Soal:

Dengan menggunakan pendekatan:


Dengan menggunakan pemfaktoran:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack L i m with x rightwards arrow 1 below fraction numerator left parenthesis 3 x minus 1 right parenthesis cubed minus left parenthesis x plus 1 right parenthesis cubed over denominator x cubed minus 1 end fraction end cell row blank equals cell stack L i m with x rightwards arrow 1 below fraction numerator left parenthesis 3 x minus 1 minus left parenthesis x plus 1 right parenthesis right parenthesis open parentheses open parentheses 3 x minus 1 close parentheses squared plus open parentheses 3 x minus 1 close parentheses open parentheses x plus 1 close parentheses plus open parentheses x plus 1 close parentheses squared close parentheses over denominator open parentheses x minus 1 close parentheses open parentheses x squared plus x plus 1 close parentheses end fraction end cell row blank equals cell stack L i m with x rightwards arrow 1 below fraction numerator open parentheses 2 x minus 2 close parentheses open parentheses open parentheses 9 x squared minus 6 x plus 1 close parentheses plus open parentheses 3 x squared plus 2 x minus 1 close parentheses plus open parentheses x squared plus 2 x plus 1 close parentheses close parentheses over denominator open parentheses x minus 1 close parentheses open parentheses x squared plus x plus 1 close parentheses end fraction end cell row blank equals cell stack L i m with x rightwards arrow 1 below fraction numerator open parentheses 2 x minus 2 close parentheses open parentheses 13 x squared minus 2 x plus 1 close parentheses over denominator open parentheses x minus 1 close parentheses open parentheses x squared plus x plus 1 close parentheses end fraction end cell row blank equals cell stack L i m with x rightwards arrow 1 below fraction numerator 2 open parentheses x minus 1 close parentheses open parentheses 13 x squared minus 2 x plus 1 close parentheses over denominator open parentheses x minus 1 close parentheses open parentheses x squared plus x plus 1 close parentheses end fraction end cell row blank equals cell stack L i m with x rightwards arrow 1 below fraction numerator 2 open parentheses 13 x squared minus 2 x plus 1 close parentheses over denominator open parentheses x squared plus x plus 1 close parentheses end fraction end cell row blank equals cell stack L i m with x rightwards arrow 1 below fraction numerator 26 x squared minus 4 x plus 2 over denominator x squared plus x plus 1 end fraction end cell row blank equals cell fraction numerator 26 left parenthesis 1 right parenthesis squared minus 4 left parenthesis 1 right parenthesis plus 2 over denominator left parenthesis 1 right parenthesis squared plus left parenthesis 1 right parenthesis plus 1 end fraction end cell row blank equals cell 24 over 3 end cell row blank equals 8 row blank blank blank row blank blank blank end table end style

Jadi, nilai dari begin mathsize 14px style stack L i m with x rightwards arrow 1 below fraction numerator open parentheses 3 x minus 1 close parentheses cubed minus open parentheses x plus 1 close parentheses cubed over denominator x cubed minus 1 end fraction end style adalah 8.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 April 2021

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