Pertanyaan

Hitunglah nilai setiap Limit berikut ini. a. x → ∞ lim 4 x 2 + 3 x − 7 8 x 2 − 6 x + 5

Hitunglah nilai setiap Limit berikut ini.

a. $x \to \infty lim \frac{8 x ^{2} - 6 x + 5}{4 x ^{2} + 3 x - 7}$

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Jawaban terverifikasi

Jawaban

.

$limit as x rightwards arrow infinity of fraction numerator 8 x squared minus 6 x plus 5 over denominator 4 x squared plus 3 x minus 7 end fraction equals 2$ .

Pembahasan

Limit Tak Hingga Fungsi Aljabar Keterangan: Diketahui . Pangkat tertinggi variabel pembilang dan penyebut adalah 2. Maka nilai adalah: Jadi, .

Limit Tak Hingga Fungsi Aljabar

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator a subscript n x to the power of n plus a subscript n minus 1 end subscript x to the power of n minus 1 end exponent plus a subscript n minus 2 end subscript x to the power of n minus 2 end exponent plus... over denominator p subscript m x to the power of m plus p subscript m minus 1 end subscript x to the power of m minus 1 end exponent plus p subscript m minus 2 end subscript x to the power of m minus 2 end exponent plus... end fraction end cell equals L row L equals cell open curly brackets table attributes columnalign left end attributes row cell L equals 0 comma space n less than m end cell row cell table row cell L equals a subscript n over p subscript m comma space n equals m end cell row cell L equals infinity comma space n greater than m end cell end table end cell end table close end cell end table end style$

Keterangan:

Diketahui $limit as x rightwards arrow infinity of fraction numerator 8 x squared minus 6 x plus 5 over denominator 4 x squared plus 3 x minus 7 end fraction$ .

Pangkat tertinggi variabel pembilang dan penyebut adalah 2.

n equals m equals 2

Maka nilai $limit as x rightwards arrow infinity of fraction numerator 8 x squared minus 6 x plus 5 over denominator 4 x squared plus 3 x minus 7 end fraction$ adalah:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 8 x squared minus 6 x plus 5 over denominator 4 x squared plus 3 x minus 7 end fraction end cell equals cell 8 over 4 end cell row blank equals 2 end table$

Jadi, $limit as x rightwards arrow infinity of fraction numerator 8 x squared minus 6 x plus 5 over denominator 4 x squared plus 3 x minus 7 end fraction equals 2$ .