Pertanyaan

x → ∞ lim x 2 + 4 x + 5 x 2 ( x 2 − 2 x + 1 ) = …

$x \to \infty lim \frac{x ^{2} ( x ^{2} - 2 x + 1 )}{x ^{2} + 4 x + 5} = \dots$

R. Subakti

Master Teacher

Mahasiswa/Alumni Universitas Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Ingat: . Dengan demikian, nilai dari limit di atas adalah . Jadi, jawaban yang tepat adalah E.

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

Dengan demikian, nilai dari limit di atas adalah begin mathsize 14px style infinity end style .

Jadi, jawaban yang tepat adalah E.