Pertanyaan

x → ∞ lim x 2 − 16 x − 3 x + 4 = ....

$x \to \infty lim \frac{x - 3 x + 4}{x ^{2} - 16} = ....$

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Habis dalam

Klaim

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

hasil dari .

hasil dari $limit as x rightwards arrow infinity of fraction numerator x minus square root of 3 x plus 4 end root over denominator x squared minus 16 end fraction equals 5 over 64$ .

Pembahasan

Untuk menyelesaikan limit fungsi tersebut dapat dengan cara metode perkalian akar sekawan sebagai berikut: Dengan demikian, hasil dari .

Untuk menyelesaikan limit fungsi tersebut dapat dengan cara metode perkalian akar sekawan sebagai berikut:

$limit as x rightwards arrow 4 of fraction numerator x minus square root of 3 x plus 4 end root over denominator open parentheses x squared minus 16 close parentheses end fraction cross times fraction numerator x plus square root of 3 x plus 4 end root over denominator open parentheses x plus square root of 3 x plus 4 end root close parentheses end fraction equals limit as x rightwards arrow 4 of fraction numerator x squared minus open parentheses 3 x plus 4 close parentheses over denominator open parentheses x squared minus 16 close parentheses open parentheses x plus square root of 3 x plus 4 end root close parentheses end fraction equals limit as x rightwards arrow 4 of fraction numerator x squared minus 3 x minus 4 over denominator open parentheses x squared minus 16 close parentheses open parentheses x plus square root of 3 x plus 4 end root close parentheses end fraction equals limit as x rightwards arrow 4 of fraction numerator open parentheses x minus 4 close parentheses open parentheses x plus 1 close parentheses over denominator open parentheses x plus 4 close parentheses open parentheses x minus 4 close parentheses open parentheses x plus square root of 3 x plus 4 end root close parentheses end fraction equals limit as x rightwards arrow 4 of fraction numerator open parentheses x plus 1 close parentheses over denominator open parentheses x plus 4 close parentheses open parentheses x plus square root of 3 x plus 4 end root close parentheses end fraction equals fraction numerator open parentheses 4 plus 1 close parentheses over denominator open parentheses 4 plus 4 close parentheses open parentheses 4 plus square root of 3 open parentheses 4 close parentheses plus 4 end root close parentheses end fraction equals fraction numerator 5 over denominator 8 open parentheses 4 plus square root of 16 close parentheses end fraction equals fraction numerator 5 over denominator 8 open parentheses 4 plus 4 close parentheses end fraction equals fraction numerator 5 over denominator 8 cross times 8 end fraction equals 5 over 64$

Dengan demikian, hasil dari $limit as x rightwards arrow infinity of fraction numerator x minus square root of 3 x plus 4 end root over denominator x squared minus 16 end fraction equals 5 over 64$ .