Pertanyaan

x → ∞ lim 5 x 4 − 2 x 3 + 1 − 5 x 4 + 8 x 2 + 7 16 x 2 − 8 x − 15 − 16 x 2 + 8 x + 5 = ...

$x \to \infty lim \frac{16 x ^{2} - 8 x - 15 - 16 x ^{2} + 8 x + 5}{5 x ^{4} - 2 x ^{3} + 1 - 5 x ^{4} + 8 x ^{2} + 7} =$ ...

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Habis dalam

Klaim

H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

$limit as x rightwards arrow infinity of space fraction numerator square root of 16 x squared minus 8 x minus 15 end root minus square root of 16 x squared plus 8 x plus 5 end root over denominator square root of 5 x to the power of 4 minus 2 x cubed plus 1 end root minus square root of 5 x to the power of 4 plus 8 x squared plus space 7 end root end fraction equals space fraction numerator limit as x rightwards arrow infinity of open parentheses square root of 16 x squared minus 8 x minus 15 end root minus square root of 16 x squared plus 8 x plus 5 end root close parentheses over denominator limit as x rightwards arrow infinity of open parentheses square root of 5 x to the power of 4 minus 2 x cubed plus 1 end root minus square root of 5 x to the power of 4 plus 8 x squared plus space 7 end root close parentheses end fraction equals space fraction numerator begin display style fraction numerator negative 8 minus 8 over denominator 2 square root of 16 end fraction end style over denominator begin display style fraction numerator negative 2 minus 8 over denominator 2 square root of 5 end fraction end style end fraction space equals space fraction numerator negative 2 over denominator negative square root of 5 end fraction space equals space 2 over 5 square root of 5$