Pertanyaan

Nilai dari x → ∞ lim ( 4 − x + x + 5 x 2 − 2 x ) adalah ...

Nilai dari $x \to \infty lim (4 - x + \frac{x ^{2} - 2 x}{x + 5})$ adalah ...

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai

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

Pembahasan

Nilai limit tak hingga dari fungsi tersebut adalah sebagai berikut. Dengan demikian, nilai

Nilai limit tak hingga dari fungsi tersebut adalah sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of space open parentheses 4 minus x plus fraction numerator x squared minus 2 x over denominator x plus 5 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of space open parentheses fraction numerator 4 open parentheses x plus 5 close parentheses over denominator x plus 5 end fraction minus fraction numerator x open parentheses x plus 5 close parentheses over denominator x plus 5 end fraction plus fraction numerator x squared minus 2 x over denominator x plus 5 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of space open parentheses fraction numerator 4 x plus 20 over denominator x plus 5 end fraction minus fraction numerator open parentheses x squared plus 5 x close parentheses over denominator x plus 5 end fraction plus fraction numerator x squared minus 2 x over denominator x plus 5 end fraction close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator negative 3 x plus 20 over denominator x plus 5 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator negative 3 x over denominator x end fraction end style plus begin display style 20 over x end style over denominator begin display style x over x end style plus begin display style 5 over x end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of space fraction numerator negative 3 plus begin display style 20 over x end style over denominator 1 plus begin display style 5 over x end style end fraction end cell row blank equals cell fraction numerator negative 3 plus 0 over denominator 1 plus 0 end fraction end cell row blank equals cell negative 3 end cell end table$

Dengan demikian, nilai $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 4 minus x plus fraction numerator x squared minus 2 x over denominator x plus 5 end fraction close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table$