Pertanyaan

x → ∞ lim ( x + ( x + p ) ( x + q ) )

$x \to \infty lim (x + (x + p) (x + q))$

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

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 open parentheses x plus square root of open parentheses x plus p close parentheses open parentheses x plus q close parentheses end root close parentheses 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 2 end table

Pembahasan

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

Nilai limit tak hingga tersebut dapat ditentukan dengan membagi semua suku dengan pangkat tertinggi dari fungsi sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of space open parentheses x plus square root of open parentheses x plus p close parentheses open parentheses x plus q close parentheses end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of space open parentheses x plus square root of x squared plus open parentheses p plus q close parentheses x plus p times q end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of space open parentheses x over x plus square root of x squared over x squared plus fraction numerator open parentheses p plus q close parentheses x over denominator x squared end fraction plus fraction numerator p q over denominator x squared end fraction end root close parentheses end cell row blank equals cell limit as x rightwards arrow infinity of space open parentheses 1 plus square root of 1 plus fraction numerator open parentheses p plus q close parentheses over denominator x end fraction plus fraction numerator p q over denominator x squared end fraction end root close parentheses end cell row blank equals cell 1 plus square root of 1 plus 0 plus 0 end root end cell row blank equals cell 1 plus square root of 1 end cell row blank equals cell 1 plus 1 end cell row blank equals 2 end table$

Dengan demikian, nilai