Pertanyaan

x → ∞ lim 2 x 2 − 1 3 x + 2 = ...

$x \to \infty lim \frac{3 x + 2}{2 x ^{2} - 1} = ...$

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Jawaban terverifikasi

Jawaban

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$limit as x rightwards arrow infinity of fraction numerator 3 x plus 2 over denominator 2 x squared minus 1 end fraction equals 0$ .

Pembahasan

Karena , dan , Maka, Jadi, .

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator a subscript n x to the power of n plus a subscript n minus 1 end subscript x to the power of n minus 1 end exponent plus..... over denominator p subscript m x to the power of m plus a subscript m minus 1 end subscript x to the power of m minus 1 end exponent plus..... end fraction end cell end table$

table attributes columnalign right center left columnspacing 0px end attributes row limit equals cell 0 space jika space straight n less than straight m end cell row blank blank blank end table

Karena table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight n end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table , m equals 2 dan n less than m ,

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

Jadi, $limit as x rightwards arrow infinity of fraction numerator 3 x plus 2 over denominator 2 x squared minus 1 end fraction equals 0$ .