Roboguru

Hitunglah setiap limit berikut ini!

Hitunglah setiap limit berikut ini!

begin mathsize 14px style limit as x rightwards arrow 8 of fraction numerator x minus 8 over denominator cube root of x minus 2 end fraction end style   

  1. ...space 

  2. ...undefined 

Jawaban:

Kita cek terlebih dahulu apakah hasil limitnya tak tentu begin mathsize 14px style open parentheses 0 over 0 close parentheses end style ;

1. Jika tidak menghasilkan tak tentu begin mathsize 14px style open parentheses 0 over 0 close parentheses end style, maka nilai tersebut adalah nilai limitnya

2. Jika ya menghasilkan tak tentu begin mathsize 14px style open parentheses 0 over 0 close parentheses end style, maka selesaikan dengan metode pemfaktoran

Cek :

begin mathsize 14px style limit as x rightwards arrow 8 of fraction numerator x minus 8 over denominator cube root of x minus 2 end fraction equals fraction numerator 8 minus 8 over denominator cube root of 8 minus 2 end fraction space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 0 over denominator 2 minus 2 end fraction space space space space space space space space space space space space space space space space space space space space space space equals 0 over 0 end style

Karena menghasilkan bentuk tak tentu, maka selesaikan dengan metode pemfaktoran.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 8 of fraction numerator x minus 8 over denominator cube root of x minus 2 end fraction end cell equals cell limit as x rightwards arrow 8 of fraction numerator open parentheses cube root of x close parentheses cubed minus open parentheses 2 close parentheses cubed over denominator cube root of x minus 2 end fraction end cell row blank equals cell limit as x rightwards arrow 8 of fraction numerator open parentheses cube root of x minus 2 close parentheses open parentheses open parentheses cube root of x close parentheses squared plus 2 cube root of x plus 2 squared close parentheses over denominator cube root of x minus 2 end fraction end cell row blank equals cell limit as x rightwards arrow 8 of left parenthesis cube root of x right parenthesis squared plus 2 cube root of x plus 4 end cell row blank equals cell left parenthesis cube root of 8 right parenthesis squared plus 2 cube root of 8 plus 2 squared end cell row blank equals cell 4 plus 4 plus 4 end cell row blank equals 12 end table end style 

Dengan demikian, begin mathsize 14px style limit as x rightwards arrow 8 of fraction numerator x minus 8 over denominator cube root of x minus 2 end fraction equals 12 end style.

0

Ruangguru

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved