Pertanyaan

Hitunglah setiap limit berikut ini! x → 27 lim 3 x − 3 x − 27

Hitunglah setiap limit berikut ini!

$x \to 27 lim \frac{x - 27}{3 x - 3}$

P. Data

Master Teacher

Jawaban terverifikasi

Jawaban

$begin mathsize 14px style limit as x rightwards arrow 27 of fraction numerator x minus 27 over denominator cube root of x minus 3 end fraction equals 27 end style$

Pembahasan

Kita cek terlebih dahulu apakah hasil limitnya tak tentu : 1. Jika tidak menghasilkan tak tentu , maka nilai tersebut adalah nilai limitnya 2. Jika ya menghasilkan tak tentu , maka selesaikan dengan metode pemfaktoran Cel : Karena menghasilkan bentuk tak tentu, maka selesaikan dengan metode pemfaktoran. Dengan demikian,

Kita cek terlebih dahulu apakah hasil limitnya tak tentu :

1. Jika tidak menghasilkan tak tentu , maka nilai tersebut adalah nilai limitnya

2. Jika ya menghasilkan tak tentu , maka selesaikan dengan metode pemfaktoran

Cel :

$begin mathsize 14px style limit as x rightwards arrow 27 of fraction numerator x minus 27 over denominator cube root of x minus 3 end fraction equals fraction numerator 27 minus 27 over denominator cube root of 27 minus 3 end fraction space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 0 over denominator 3 minus 3 end fraction space space space space space space space space space space space space space space space space space space space space space space space equals 0 over 0 end style$

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

$begin mathsize 14px style limit as x rightwards arrow 27 of fraction numerator x minus 27 over denominator cube root of x minus 3 end fraction equals limit as x rightwards arrow 27 of fraction numerator open parentheses cube root of x close parentheses cubed minus open parentheses 3 close parentheses cubed over denominator cube root of x minus 3 end fraction space space space space space space space space space space space space space space space space space space space space space space space equals limit as x rightwards arrow 27 of fraction numerator open parentheses cube root of x minus 3 close parentheses open parentheses open parentheses cube root of x close parentheses squared plus 3 times cube root of x plus 3 squared close parentheses over denominator cube root of x minus 3 end fraction space space space space space space space space space space space space space space space space space space space space space space space equals limit as x rightwards arrow 27 of open parentheses open parentheses cube root of x close parentheses squared plus 3 times cube root of x plus 3 squared close parentheses space space space space space space space space space space space space space space space space space space space space space space space equals open parentheses cube root of 27 close parentheses squared plus 3 times cube root of 27 plus 9 space space space space space space space space space space space space space space space space space space space space space space space equals 9 plus 9 plus 9 space space space space space space space space space space space space space space space space space space space space space space space equals 27 end style$

Dengan demikian, $begin mathsize 14px style limit as x rightwards arrow 27 of fraction numerator x minus 27 over denominator cube root of x minus 3 end fraction equals 27 end style$