Pertanyaan

x → 2 lim ​ x 2 + 5 x + 6 x 2 − 10 x − 24 ​ = ....

 = ....

R. Novianto

Master Teacher

Mahasiswa/Alumni Universitas Tanjungpura Pontianak

Jawaban terverifikasi

Jawaban

  begin mathsize 14px style limit as straight x rightwards arrow 2 of fraction numerator straight x squared minus 10 straight x minus 24 over denominator straight x squared plus 5 straight x plus 6 end fraction equals negative 2 over 3 end style  

Pembahasan

soal di atas merupakan limit tak tentu fungsi aljabar yang penyelesaiannya menggunakan dalil L'hospital, yaitu dengan menggunakan turunan. Perhatikan perhitungan berikut ! Jadi,

soal di atas merupakan limit tak tentu fungsi aljabar yang penyelesaiannya menggunakan dalil L'hospital, yaitu dengan menggunakan turunan.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as straight x rightwards arrow straight a of fraction numerator straight f open parentheses straight x close parentheses over denominator straight g open parentheses straight x close parentheses end fraction end cell cell equals limit as straight x rightwards arrow straight a of end cell cell fraction numerator straight f apostrophe open parentheses straight x close parentheses over denominator straight g apostrophe open parentheses straight x close parentheses end fraction end cell end table end style 

Perhatikan perhitungan berikut !
 

 begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell limit as straight x rightwards arrow 2 of fraction numerator straight x squared minus 10 straight x minus 24 over denominator straight x squared plus 5 straight x plus 6 end fraction end cell equals cell limit as straight x rightwards arrow 2 of fraction numerator 2 straight x minus 10 over denominator 2 straight x plus 5 end fraction end cell row blank equals cell fraction numerator 2 open parentheses 2 close parentheses minus 10 over denominator 2 open parentheses 2 close parentheses plus 5 end fraction end cell row blank equals cell fraction numerator 4 minus 10 over denominator 4 plus 5 end fraction end cell row blank equals cell fraction numerator negative 6 over denominator 9 end fraction end cell row blank equals cell negative 6 over 9 end cell row blank equals cell negative 2 over 3 end cell end table end style  
 

Jadi,  begin mathsize 14px style limit as straight x rightwards arrow 2 of fraction numerator straight x squared minus 10 straight x minus 24 over denominator straight x squared plus 5 straight x plus 6 end fraction equals negative 2 over 3 end style  

118

3.6 (3 rating)

Hasna Amalia

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