Pertanyaan

Hitunglah nilai limit berikut! 5. x → ∞ lim x 2 + 5 x + 2 2 x 2 + 7 x + 6 = ....

Hitunglah nilai limit berikut!

5. $x \to \infty lim \frac{2 x ^{2} + 7 x + 6}{x ^{2} + 5 x + 2} = ....$

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Dengan menggunakan metode membagi pangkat tertinggi,

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator 2 x squared plus 7 x plus 6 over denominator x squared plus 5 x plus 2 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 2 up diagonal strike x squared end strike over denominator up diagonal strike x squared end strike end fraction end style plus begin display style fraction numerator 7 up diagonal strike x over denominator x to the power of up diagonal strike 2 end exponent end fraction end style plus begin display style 6 over x squared end style over denominator begin display style fraction numerator up diagonal strike x squared end strike over denominator up diagonal strike x squared end strike end fraction end style plus begin display style fraction numerator 5 up diagonal strike x over denominator x to the power of up diagonal strike 2 end exponent end fraction end style plus begin display style 2 over x squared end style end fraction space end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 2 plus begin display style 7 over x end style plus begin display style 6 over x squared end style over denominator 1 plus begin display style 5 over x end style plus begin display style 2 over x squared end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 2 plus 7 times begin display style 1 over x end style plus begin display style 6 times 1 over x squared end style over denominator 1 plus 5 times begin display style 1 over x end style plus 2 times begin display style 1 over x squared end style end fraction space rightwards arrow teorema space limit as x rightwards arrow infinity of 1 over x to the power of n equals 0 end cell row blank equals cell fraction numerator 2 plus 7 times 0 plus 6 times 0 over denominator 1 plus 5 times 0 plus 2 times 0 end fraction end cell row blank equals cell 2 over 1 end cell row blank equals 2 end table end style$