Pertanyaan

Nilai dari x → ∞ lim x 2 + 3 2 x 2 + x − 12 = ... .

Nilai dari $x \to \infty lim \frac{2 x ^{2} + x - 12}{x ^{2} + 3} = ...$ .

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Ingat: . Jadi Oleh karena itu, jawaban yang tepat adalah C.

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 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator 2 x squared plus x minus 12 over denominator x squared plus 3 end fraction end cell equals cell limit as x rightwards arrow infinity of space fraction numerator 2 x squared plus x minus 12 over denominator x squared plus 3 end fraction cross times fraction numerator begin display style 1 over x squared end style over denominator 1 over x squared end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator begin display style fraction numerator 2 x squared over denominator x squared end fraction plus x over x squared minus 12 over x squared end style over denominator begin display style x squared over x squared plus 3 over x squared end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator 2 plus begin display style 1 over x end style minus begin display style 12 over x squared end style over denominator 1 plus begin display style 3 over x squared end style end fraction end cell row blank equals cell fraction numerator 2 plus begin display style 1 over infinity end style minus begin display style 12 over infinity squared end style over denominator 1 plus begin display style 3 over infinity squared end style end fraction end cell row blank equals cell fraction numerator 2 plus 0 minus 0 over denominator 1 plus 0 end fraction end cell row blank equals 2 end table$

Jadi $table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of space fraction numerator 2 x squared plus x minus 12 over denominator x squared plus 3 end fraction end cell equals 2 end table$

Oleh karena itu, jawaban yang tepat adalah C.