Tentukan nilai x→1lim​x3−1(3x−1)3−(x+1)3​ dengan menunjukkan pendekatan nilai dan proses pergantian fungsi dengan faktorisasi!

Pertanyaan

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

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F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai limit tersebut saat mendekati satu = 8

Pembahasan

Pembahasan

Cara pendekatan Nilai untuk  

Jadi nilai limit tersebut saat mendekati satu = 8

 

Cara faktorisasi

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of 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 cell equals cell limit as x rightwards arrow 1 of fraction numerator left parenthesis left parenthesis 3 x minus 1 right parenthesis minus left parenthesis x plus 1 right parenthesis right parenthesis left parenthesis left parenthesis 3 x minus 1 right parenthesis squared plus left parenthesis 3 x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis plus left parenthesis x plus 1 right parenthesis squared right parenthesis over denominator left parenthesis x minus 1 right parenthesis left parenthesis x squared plus x times 1 plus 1 squared right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 2 left parenthesis x minus 1 right parenthesis left parenthesis left parenthesis 3 x minus 1 right parenthesis squared plus left parenthesis 3 x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis plus left parenthesis x plus 1 right parenthesis squared right parenthesis over denominator left parenthesis x minus 1 right parenthesis left parenthesis x squared plus x times 1 plus 1 squared right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow 1 of fraction numerator 2 left parenthesis left parenthesis 3 x minus 1 right parenthesis squared plus left parenthesis 3 x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis plus left parenthesis x plus 1 right parenthesis squared right parenthesis over denominator left parenthesis x squared plus x times 1 plus 1 squared right parenthesis end fraction end cell row blank equals cell fraction numerator 2 left parenthesis left parenthesis 3 left parenthesis 1 right parenthesis minus 1 right parenthesis squared plus left parenthesis 3 left parenthesis 1 right parenthesis minus 1 right parenthesis left parenthesis 1 plus 1 right parenthesis plus left parenthesis 1 plus 1 right parenthesis squared right parenthesis over denominator left parenthesis 1 squared plus 1 times 1 plus 1 squared right parenthesis end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 12 right parenthesis over denominator 3 end fraction end cell row blank equals 8 end table end style

Jadi nilai limit tersebut saat mendekati satu = 8

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