Pertanyaan

Hitunglah! 1. x → ∞ lim 4 x 4 + 3 x + 2 3 x 5 + 2 x − 1 = ...

Hitunglah!

1. $x \to \infty lim \frac{3 x ^{5} + 2 x - 1}{4 x ^{4} + 3 x + 2} = ...$

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R. Subakti

Master Teacher

Mahasiswa/Alumni Universitas Indonesia

Jawaban terverifikasi

Jawaban

Pembahasan

Ingat: . Jadi

Ingat: limit as x rightwards arrow infinity of k over x to the power of n equals k over infinity to the power of n equals 0 .

$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 5 plus 2 x minus 1 over denominator 4 x to the power of 4 plus 3 x plus 2 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator 3 x to the power of 5 plus 2 x minus 1 over denominator 4 x to the power of 4 plus 3 x plus 2 end fraction cross times fraction numerator begin display style 1 over x to the power of 5 end style over denominator begin display style 1 over x to the power of 5 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 3 x to the power of 5 over denominator x to the power of 5 end fraction end style plus begin display style fraction numerator 2 x over denominator x to the power of 5 end fraction end style minus begin display style 1 over x to the power of 5 end style over denominator begin display style fraction numerator 4 x to the power of 4 over denominator x to the power of 5 end fraction end style plus begin display style fraction numerator 3 x over denominator x to the power of 5 end fraction end style plus begin display style 2 over x to the power of 5 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 to the power of 4 minus 1 over x to the power of 5 end style over denominator begin display style 4 over x plus 3 over x to the power of 4 plus 2 over x to the power of 5 end style end fraction end cell row blank equals cell fraction numerator begin display style 3 plus 2 over infinity to the power of 4 minus 1 over infinity to the power of 5 end style over denominator begin display style 4 over infinity plus 3 over infinity to the power of 4 plus 2 over infinity to the power of 5 end style end fraction end cell row blank equals cell fraction numerator 3 plus 0 minus 0 over denominator 0 plus 0 plus 0 end fraction end cell row blank equals infinity end table$

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