Pertanyaan

Nilai x → ∞ lim 2 x 5 − 4 x + 3 x 2 + 4 − 3 x + 3 x 2 = ...

Nilai $x \to \infty lim \frac{5 - 4 x + 3 x ^{2} + 4 - 3 x + 3 x ^{2}}{2 x} = ...$

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Jawaban terverifikasi

Jawaban

nilai

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

Pembahasan

Nilai limit tak hingga dari fungsi tersebut dapat ditentukan dengan membagi semua suku dengan di mana merupakan pangkat tertinggi dari fungsi sebagai berikut. Dengan demikian, nilai

Nilai limit tak hingga dari fungsi tersebut dapat ditentukan dengan membagi semua suku dengan x to the power of n di mana merupakan pangkat tertinggi dari fungsi sebagai berikut.

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

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