Pertanyaan

Tentukan nilai: X → ∞ lim ( x + 6 x − x − 2 x )

Tentukan nilai:

$X \to \infty lim (x + 6 x - x - 2 x)$

D. Entry

Master Teacher

Jawaban terverifikasi

Pembahasan

Dengan menerapkan konsep perkalian sekawan: Pangkat terbesar dari fungsi adalah atau maka pembilang dan penyebut di bagi oleh , sehingga diperoleh: Jadi, Nilai

Dengan menerapkan konsep perkalian sekawan:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as straight x rightwards arrow infinity of left parenthesis square root of straight x plus 6 square root of straight x end root minus square root of straight x minus 2 square root of straight x end root right parenthesis end cell row blank equals cell limit as straight x rightwards arrow infinity of left parenthesis square root of straight x plus 6 square root of straight x end root minus square root of straight x minus 2 square root of straight x end root right parenthesis times fraction numerator left parenthesis square root of straight x plus 6 square root of straight x end root plus square root of straight x minus 2 square root of straight x end root right parenthesis over denominator left parenthesis square root of straight x plus 6 square root of straight x end root plus square root of straight x minus 2 square root of straight x end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator straight x plus 6 square root of straight x minus left parenthesis straight x minus 2 square root of straight x right parenthesis over denominator left parenthesis square root of straight x plus 6 square root of straight x end root plus square root of straight x minus 2 square root of straight x end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator straight x plus 6 square root of straight x minus straight x plus 2 square root of straight x over denominator left parenthesis square root of straight x plus 6 square root of straight x end root plus square root of straight x minus 2 square root of straight x end root right parenthesis end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator 8 square root of straight x over denominator left parenthesis square root of straight x plus 6 square root of straight x end root plus square root of straight x minus 2 square root of straight x end root right parenthesis end fraction end cell end table end style$

Pangkat terbesar dari fungsi $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 8 square root of straight x over denominator left parenthesis square root of straight x plus 6 square root of straight x end root plus square root of straight x minus 2 square root of straight x end root right parenthesis end fraction end cell end table$ adalah atau maka pembilang dan penyebut di bagi oleh , sehingga diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight x rightwards arrow infinity of fraction numerator 8 square root of straight x over denominator left parenthesis square root of straight x plus 6 square root of straight x end root plus square root of straight x minus 2 square root of straight x end root right parenthesis end fraction end cell equals cell limit as straight x rightwards arrow infinity of fraction numerator begin display style fraction numerator 8 square root of straight x over denominator square root of straight x end fraction end style over denominator begin display style fraction numerator left parenthesis square root of straight x plus 6 square root of straight x end root plus square root of straight x minus 2 square root of straight x end root right parenthesis over denominator square root of straight x end fraction end style end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator begin display style 8 end style over denominator begin display style fraction numerator begin display style left parenthesis square root of straight x plus 6 square root of straight x end root end style over denominator square root of straight x end fraction plus fraction numerator begin display style square root of straight x minus 2 square root of straight x end root right parenthesis end style over denominator square root of straight x end fraction end style end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator begin display style 8 end style over denominator begin display style square root of fraction numerator straight x plus 6 square root of straight x over denominator straight x end fraction end root plus square root of fraction numerator straight x minus 2 square root of straight x over denominator straight x end fraction end root end style end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator begin display style 8 end style over denominator begin display style square root of straight x over straight x plus fraction numerator 6 square root of straight x over denominator straight x end fraction end root plus square root of straight x over straight x minus fraction numerator 2 square root of straight x over denominator straight x end fraction end root end style end fraction end cell row blank equals cell limit as straight x rightwards arrow infinity of fraction numerator begin display style 8 end style over denominator begin display style square root of 1 plus fraction numerator 6 over denominator square root of straight x end fraction end root plus square root of 1 minus fraction numerator 2 over denominator square root of straight x end fraction end root end style end fraction end cell row blank equals cell fraction numerator begin display style 8 end style over denominator begin display style square root of 1 plus fraction numerator 6 over denominator square root of infinity end fraction end root plus square root of 1 minus fraction numerator 2 over denominator square root of infinity end fraction end root end style end fraction end cell row blank equals cell fraction numerator begin display style 8 end style over denominator begin display style square root of 1 plus 0 end root plus square root of 1 minus 0 end root end style end fraction end cell row blank equals cell 8 over 2 end cell row blank equals 4 end table$

Jadi, Nilai limit as straight X rightwards arrow infinity of left parenthesis square root of straight x plus 6 square root of straight x end root minus square root of straight x minus 2 square root of straight x end root right parenthesis equals 4