Pertanyaan

x → ∞ lim 6 x 4 − 7 x + 9 2 x 3 + 6 x 2 + 7 x − 5 = …

$x \to \infty lim \frac{2 x ^{3} + 6 x ^{2} + 7 x - 5}{6 x ^{4} - 7 x + 9} = \dots$

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Jawaban terverifikasi

Jawaban

nilai adalah 0.

nilai $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator 2 x cubed plus 6 x squared plus 7 x minus 5 over denominator 6 x to the power of 4 minus 7 x plus 9 end fraction end cell end table$ adalah 0.

Pembahasan

Konsep limit tak hingga fungsi rasional adalah denganmetode membagi dengan pangkat tertinggi Diketahui: Pangkat tertinggi adalah , maka pembilang dan penyebut dibagi oleh , maka diperoleh penyelesaiannyasebagai berikut: Jadi, nilai adalah 0.

Konsep limit tak hingga fungsi rasional adalah dengan metode membagi dengan pangkat tertinggi

Diketahui: $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator 2 x cubed plus 6 x squared plus 7 x minus 5 over denominator 6 x to the power of 4 minus 7 x plus 9 end fraction end cell end table$

Pangkat tertinggi adalah x to the power of 4 , maka pembilang dan penyebut dibagi oleh , maka diperoleh penyelesaiannya sebagai berikut:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 2 x cubed plus 6 x squared plus 7 x minus 5 over denominator 6 x to the power of 4 minus 7 x plus 9 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 2 x cubed over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 6 x squared over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 7 x over denominator x to the power of 4 end fraction end style minus begin display style 5 over x to the power of 4 end style over denominator begin display style fraction numerator 6 x to the power of 4 over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 7 x over denominator x to the power of 4 end fraction end style plus begin display style 9 over x to the power of 4 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 2 over x plus 6 over x squared plus 7 over x cubed minus 5 over x to the power of 4 end style over denominator begin display style 6 minus 7 over x cubed plus 9 over x to the power of 4 end style end fraction end cell row blank equals cell fraction numerator 0 plus 0 plus 0 minus 0 over denominator 6 minus 0 plus 0 end fraction end cell row blank equals cell 0 over 6 end cell row blank equals 0 end table$

Jadi, nilai $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator 2 x cubed plus 6 x squared plus 7 x minus 5 over denominator 6 x to the power of 4 minus 7 x plus 9 end fraction end cell end table$ adalah 0.