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x→∞lim​x3−5x4+2x−23x4+2x​=...

Pertanyaan

begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator 3 x to the power of 4 plus 2 x over denominator x cubed minus 5 x to the power of 4 plus 2 x minus 2 end fraction equals end style...

M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style 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 3 x to the power of 4 plus 2 x over denominator x cubed minus 5 x to the power of 4 plus 2 x minus 2 end fraction end cell end table equals negative 3 over 5 end style.

Pembahasan

Gunakan konsep limit tak hingga, bagilah dengan suku tertinggi. Oleh karena limit menuju tak hingga maka ambil nilai limit yang tidak mengandung variabel seperti berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 3 x to the power of 4 plus 2 x over denominator x cubed minus 5 x to the power of 4 plus 2 x minus 2 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 3 x to the power of 4 over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 2 x over denominator x to the power of 4 end fraction end style over denominator begin display style x cubed over x to the power of 4 end style minus begin display style fraction numerator 5 x to the power of 4 over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 2 x over denominator x to the power of 4 end fraction end style minus begin display style 2 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 3 plus 2 over x cubed end style over denominator begin display style 1 over x minus 5 plus 2 over x cubed minus 2 over x to the power of 4 end style end fraction end cell row blank equals cell fraction numerator begin display style 3 plus 0 end style over denominator begin display style 0 minus 5 plus 0 minus 0 end style end fraction end cell row blank equals cell negative 3 over 5 end cell end table 

Dengan demikian begin mathsize 14px style 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 3 x to the power of 4 plus 2 x over denominator x cubed minus 5 x to the power of 4 plus 2 x minus 2 end fraction end cell end table equals negative 3 over 5 end style.

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