Pertanyaan

Tentukan nilai limit berikut! a. x → ∞ lim ( 5 − x 3 x + 2 ) 3

Tentukan nilai limit berikut!

a. $x \to \infty lim (\frac{3 x + 2}{5 - x})^{3}$

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Limit menuju tak hingga, karena pangkat tertinggi sama maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses fraction numerator 3 x plus 2 over denominator 5 minus x end fraction close parentheses cubed end cell equals cell open parentheses fraction numerator 3 x plus 2 over denominator 5 minus x end fraction close parentheses squared open parentheses fraction numerator 3 x plus 2 over denominator 5 minus x end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 9 x squared plus 12 x plus 4 over denominator 25 minus 10 x plus x squared end fraction close parentheses open parentheses fraction numerator 3 x plus 2 over denominator 5 minus x end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 27 x cubed plus 54 x squared plus 36 x plus 8 over denominator 125 minus 75 x plus 15 x squared minus x cubed end fraction close parentheses end cell row blank equals cell fraction numerator 27 over denominator negative 1 end fraction end cell end table end style$

Limit menuju tak hingga, karena pangkat tertinggi sama maka $begin mathsize 14px style limit as x rightwards arrow infinity of open parentheses fraction numerator 3 x plus 2 over denominator 5 minus x end fraction close parentheses cubed equals negative 27 end style$