Pertanyaan

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

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

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hasil dari adalah .

hasil dari $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x to the power of 4 plus 3 x squared minus 7 x over denominator 3 x squared minus 6 x to the power of 4 minus 9 end fraction end cell end table$ adalah negative 1 third

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, hasil dari adalah .

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

Diketahui: $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x to the power of 4 plus 3 x squared minus 7 x over denominator 3 x squared minus 6 x to the power of 4 minus 9 end fraction end cell end table$

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

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 2 x to the power of 4 plus 3 x squared minus 7 x over denominator 3 x squared minus 6 x to the power of 4 minus 9 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses begin display style fraction numerator 2 x to the power of 4 over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 3 x squared over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 7 x over denominator x to the power of 4 end fraction end style close parentheses over denominator open parentheses begin display style fraction numerator 3 x squared over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 6 x to the power of 4 over denominator x to the power of 4 end fraction end style minus begin display style 9 over x to the power of 4 end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 2 plus begin display style 3 over x squared end style minus begin display style 7 over x cubed end style over denominator begin display style 3 over x squared end style minus 6 minus begin display style 9 over x to the power of 4 end style end fraction end cell row blank equals cell fraction numerator 2 plus 0 minus 0 over denominator 0 minus 6 minus 0 end fraction end cell row blank equals cell fraction numerator 2 over denominator negative 6 end fraction end cell row blank equals cell negative 1 third end cell end table$

Jadi, hasil dari $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x to the power of 4 plus 3 x squared minus 7 x over denominator 3 x squared minus 6 x to the power of 4 minus 9 end fraction end cell end table$ adalah .