Pertanyaan

Nilai dari x → ∞ lim 2 x 4 − 2 x 2 + 3 4 x 4 − 2 x + 1 adalah ....

Nilai dari $x \to \infty lim \frac{4 x ^{4} - 2 x + 1}{2 x ^{4} - 2 x ^{2} + 3}$ adalah ....

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P. Afrisno

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

tidak ada pilihan jawaban yang benar.

Pembahasan

Ingat kembali konsep limit tak hingga berikut. Sehingga dapat ditentukan: Dengan demikian diperoleh . Jadi, tidak ada pilihan jawaban yang benar.

Ingat kembali konsep limit tak hingga berikut.

limit as x rightwards arrow infinity of c over x to the power of n equals 0

Sehingga dapat ditentukan:

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

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

Jadi, tidak ada pilihan jawaban yang benar.