Pertanyaan

x → ∞ lim ( 2 x + 2 − 2 x − 1 ) ( 2 x + 5 ) =

$x \to \infty lim (2 x + 2 - 2 x - 1) (2 x + 5) =$

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style limit as x rightwards arrow infinity of square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root space a equals p rightwards double arrow fraction numerator b minus q over denominator 2 square root of a end fraction limit as x rightwards arrow infinity of left parenthesis square root of 2 x plus 2 end root minus square root of 2 x minus 1 end root right parenthesis left parenthesis square root of 2 x plus 5 end root right parenthesis equals limit as x rightwards arrow infinity of left parenthesis square root of 2 x plus 2 end root right parenthesis left parenthesis square root of 2 x plus 5 end root right parenthesis minus left parenthesis square root of 2 x minus 1 end root right parenthesis left parenthesis square root of 2 x plus 5 end root right parenthesis equals limit as x rightwards arrow infinity of square root of open parentheses 2 x plus 2 close parentheses open parentheses 2 x plus 5 close parentheses end root minus square root of open parentheses 2 x minus 1 close parentheses open parentheses 2 x plus 5 close parentheses end root equals limit as x rightwards arrow infinity of square root of 4 x squared plus 14 x plus 10 end root minus square root of 4 x squared plus 8 x minus 5 end root equals fraction numerator b minus q over denominator 2 square root of a end fraction equals fraction numerator 14 minus 8 over denominator 2 square root of 4 end fraction equals 6 over 4 equals 3 over 2 end style$