Pertanyaan

Nilai dari x → ∞ lim 2 x 4 + 5 x 2 − 1 ( 2 x − 3 x 3 ) ( 1 + x ) = ....

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

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D

Pembahasan

Diberikan suatu limit: . Penyelesaian limit tersebut yaitu membaginya dengan variabel pangkat tertinggi: Jadi, jawaban yang tepat adalah D

Diberikan suatu limit: $begin mathsize 14px style limit as x rightwards arrow infinity of fraction numerator open parentheses 2 x minus 3 x cubed close parentheses open parentheses 1 plus x close parentheses over denominator 2 x to the power of 4 plus 5 x squared minus 1 end fraction end style$ .

Penyelesaian limit tersebut yaitu membaginya dengan variabel pangkat tertinggi:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator negative 3 x to the power of 4 minus 3 x cubed plus 2 x squared plus 2 x over denominator 2 x to the power of 4 plus 5 x squared minus 1 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator negative 3 x to the power of 4 over denominator x to the power of 4 end fraction end style minus begin display style fraction numerator 3 x cubed over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 2 x squared over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 2 x over denominator x to the power of 4 end fraction end style over denominator begin display style fraction numerator 2 x to the power of 4 over denominator x to the power of 4 end fraction end style plus begin display style fraction numerator 5 x squared over denominator x to the power of 4 end fraction end style minus begin display style 1 over x to the power of 4 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style negative 3 minus 3 over x plus 2 over x squared plus 2 over x cubed end style over denominator begin display style 2 plus 5 over x squared minus 1 over x to the power of 4 end style end fraction end cell row blank equals cell fraction numerator negative 3 minus 3 over infinity plus 2 over infinity plus 2 over infinity over denominator 2 plus 5 over infinity minus 1 over infinity end fraction end cell row blank equals cell fraction numerator negative 3 minus 0 plus 0 plus 0 over denominator 2 plus 0 minus 0 end fraction end cell row blank equals cell negative 3 over 2 end cell end table end style$

Jadi, jawaban yang tepat adalah D