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Tentukan nilai limit berikut!

a. 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 end style

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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Pembahasan

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 begin mathsize 14px style x end style 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 

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