Pertanyaan

x → ∞ lim 4 x 4 + 9 x 3 + 7 − 4 x 4 + 4 x 2 − 5 = ....

$x \to \infty lim 4 x^{4} + 9 x^{3} + 7 - 4 x^{4} + 4 x^{2} - 5 = ....$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

hasil dari adalah

hasil dari limit as x rightwards arrow infinity of square root of 4 x to the power of 4 plus 9 x cubed plus 7 end root minus square root of 4 x to the power of 4 plus 4 x squared minus 5 end root equals 0

limit as x rightwards arrow infinity of square root of 4 x to the power of 4 plus 9 x cubed plus 7 end root minus square root of 4 x to the power of 4 plus 4 x squared minus 5 end root equals 0

adalah

Pembahasan

Cara 1: Cara 2: Ingat kembali: Sehingga diperoleh perhitungan, Karena maka Jadi, hasil dari adalah

Cara 1:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of square root of 4 x to the power of 4 plus 9 x cubed plus 7 end root minus square root of 4 x to the power of 4 plus 4 x squared minus 5 end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of 4 x to the power of 4 plus 9 x cubed plus 7 end root minus square root of 4 x to the power of 4 plus 4 x squared minus 5 end root end cell row blank blank cell cross times fraction numerator square root of 4 x to the power of 4 plus 9 x cubed plus 7 end root plus square root of 4 x to the power of 4 plus 4 x squared minus 5 end root over denominator square root of 4 x to the power of 4 plus 9 x cubed plus 7 end root plus square root of 4 x to the power of 4 plus 4 x squared minus 5 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses square root of 4 x to the power of 4 plus 9 x cubed plus 7 end root close parentheses squared minus open parentheses square root of 4 x to the power of 4 plus 4 x squared minus 5 end root close parentheses squared over denominator square root of 4 x to the power of 4 plus 9 x cubed plus 7 end root plus square root of 4 x to the power of 4 plus 4 x squared minus 5 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 4 x to the power of 4 plus 9 x cubed plus 7 minus 4 x to the power of 4 minus 4 x squared plus 5 over denominator square root of 4 x to the power of 4 plus 9 x cubed plus 7 end root plus square root of 4 x to the power of 4 plus 4 x squared minus 5 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 9 x cubed minus 4 x squared plus 12 over denominator square root of 4 x to the power of 4 plus 9 x cubed plus 7 end root plus square root of 4 x to the power of 4 plus 4 x squared minus 5 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 9 x cubed over denominator x cubed end fraction end style minus begin display style fraction numerator 4 x squared over denominator x cubed end fraction end style plus begin display style 12 over x cubed end style over denominator square root of fraction numerator 4 x to the power of 4 over denominator x to the power of 6 end fraction plus fraction numerator 9 x cubed over denominator x to the power of 6 end fraction plus 7 over x to the power of 6 end root plus square root of fraction numerator 4 x to the power of 4 over denominator x to the power of 6 end fraction plus fraction numerator 4 x squared over denominator x to the power of 6 end fraction minus 5 over x to the power of 6 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 9 minus 4 over x plus 12 over x cubed end style over denominator square root of 4 over x squared plus 9 over x cubed plus 7 over x to the power of 6 end root plus square root of 4 over x squared plus 4 over x to the power of 4 minus 5 over x to the power of 6 end root end fraction end cell row blank equals cell fraction numerator begin display style 9 minus 4 over infinity plus 12 over infinity cubed end style over denominator square root of 4 over infinity squared plus 9 over infinity cubed plus 7 over infinity to the power of 6 end root plus square root of 4 over infinity squared plus 4 over infinity to the power of 4 minus 5 over infinity to the power of 6 end root end fraction end cell row blank equals cell fraction numerator begin display style 9 minus 0 plus 0 end style over denominator square root of 0 plus 0 plus 0 end root plus square root of 0 plus 0 minus 0 end root end fraction end cell row blank equals cell 9 over 0 end cell row blank equals infinity row blank blank blank end table$

Cara 2:

Ingat kembali:

$limit as x rightwards arrow infinity of fraction numerator a x to the power of m plus b x to the power of m minus 1 end exponent plus... plus c over denominator p x to the power of n plus q x to the power of n minus 1 end exponent plus... plus r end fraction equals L L equals 0 space a p a b i l a space m less than n L equals m over n comma space a p a b i l a space m equals n L equals infinity comma space a p a b i l a space m greater than n$

Sehingga diperoleh perhitungan,

Karena m greater than n maka L equals infinity

Jadi, hasil dari limit as x rightwards arrow infinity of square root of 4 x to the power of 4 plus 9 x cubed plus 7 end root minus square root of 4 x to the power of 4 plus 4 x squared minus 5 end root equals 0 adalah