Pertanyaan

Carilah nilai limit tak hingga berikut ! x → ∞ lim 5 x 3 + 8 x 2 + 6 4 x 3 + 2 x + 1

Carilah nilai limit tak hingga berikut !

$x \to \infty lim \frac{4 x ^{3} + 2 x + 1}{5 x ^{3} + 8 x ^{2} + 6}$

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Pembahasan

Pada limit tak hingga berlaku Maka pada pangkat tertinggi pada pembilang dan penyebut sama sehingga :

Pada limit tak hingga berlaku

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

Maka pada $begin mathsize 14px style limit as straight x rightwards arrow infinity of fraction numerator 4 straight x cubed plus 2 straight x plus 1 over denominator 5 straight x cubed plus 8 straight x squared plus 6 end fraction end style$ pangkat tertinggi pada pembilang dan penyebut sama sehingga :

$limit as straight x rightwards arrow infinity of fraction numerator 4 straight x cubed plus 2 straight x plus 1 over denominator 5 straight x cubed plus 8 straight x squared plus 6 end fraction equals limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 4 x cubed over denominator x cubed end fraction end style plus begin display style fraction numerator 2 x over denominator x cubed end fraction end style plus begin display style 1 over x cubed end style over denominator begin display style fraction numerator 5 x cubed over denominator x cubed end fraction end style plus begin display style fraction numerator 8 x squared over denominator x cubed end fraction end style plus begin display style 6 over x cubed end style end fraction equals limit as x rightwards arrow infinity of fraction numerator begin display style 4 plus 2 over x squared plus 1 over x cubed end style over denominator begin display style 5 plus 8 over x plus 6 over x cubed end style end fraction equals fraction numerator 4 plus 0 plus 0 over denominator 5 plus 0 plus 0 end fraction equals 4 over 5$