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Nilai dari x→∞lim​x2−2x+32x2+6x+1​ adalah ...

Pertanyaan

Nilai dari limit as x rightwards arrow infinity of fraction numerator 2 x squared plus 6 x plus 1 over denominator x squared minus 2 x plus 3 end fraction adalah ...

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Langkah pertama untuk menentukan nilai limit 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 2 x squared plus 6 x plus 1 over denominator x squared minus 2 x plus 3 end fraction end cell end table adalah membagi setiap suku dengan variabel pangkat tertinggi. Variabel pangkat tertinggi pada bentuk limit tersebut adalah x squared, maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 2 x squared plus 6 x plus 1 over denominator x squared minus 2 x plus 3 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 2 x squared over denominator x squared end fraction end style plus begin display style fraction numerator 6 x over denominator x squared end fraction end style plus begin display style 1 over x squared end style over denominator begin display style x squared over x squared end style minus begin display style fraction numerator 2 x over denominator x squared end fraction end style plus begin display style 3 over x squared end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 2 plus 6 over x plus 1 over x squared end style over denominator begin display style 1 minus 2 over x plus 3 over x squared end style end fraction end cell row blank equals cell fraction numerator 2 plus 0 plus 0 over denominator 1 minus 0 plus 0 end fraction end cell row blank equals cell 2 over 1 end cell row blank equals 2 end table

Jadi, nilai 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 2 x squared plus 6 x plus 1 over denominator x squared minus 2 x plus 3 end fraction end cell end tableadalah 2.

Oleh karena itu, jawaban yang benar adalah B.

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