Pertanyaan

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

Tentukan nilai $x \to 1 lim \frac{( 3 x - 1 ) ^{3} - ( x + 1 ) ^{3}}{x ^{3} - 1}$ dengan menunjukkan pendekatan nilai dan proses pergantian fungsi dengan faktorisasi!

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai limit tersebut saat mendekati satu = 8

Pembahasan

Cara pendekatan Nilai untuk Jadi nilai limit tersebut saat mendekati satu = 8 Cara faktorisasi Jadi nilai limit tersebut saat mendekati satu = 8

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