Pertanyaan

x → ∞ lim ( 2 + x ) ( 3 − x ) ( 2 + 4 x ) ( 2 − x ) = …

$x \to \infty lim \frac{( 2 + 4 x ) ( 2 - x )}{( 2 + x ) ( 3 - x )} = \dots$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai limit di atas adalah 4

Pembahasan

Untuk menentukan limit di atas dapat menggunakan konseplimit tak hinggga bentuk fungsi rasional, yaitu dengan membagi pembilang dan penyebut dengan variabel yang memiliki pangkat tertinggi di penyebut Sehingga : Jadi, nilai limit di atas adalah 4

$space space space space space limit as x rightwards arrow infinity of fraction numerator left parenthesis 2 plus 4 x right parenthesis left parenthesis 2 minus x right parenthesis over denominator left parenthesis 2 plus x right parenthesis left parenthesis 3 minus x right parenthesis end fraction equals limit as x rightwards arrow infinity of fraction numerator negative 4 x squared plus 6 x plus 4 over denominator negative x squared plus x plus 6 end fraction$

Untuk menentukan limit di atas dapat menggunakan konsep limit tak hinggga bentuk fungsi rasional, yaitu dengan membagi pembilang dan penyebut dengan variabel yang memiliki pangkat tertinggi di penyebut

P e n y e b u t space p a d a space s o a l space equals space minus x squared plus x plus 6 comma space m a k a space v a r i a b e l space y a n g space m e m i l i k i space p a n g k a t space t e r t i n g g i space a d a l a h space x squared

Sehingga :

$space space space space space space space space limit as x rightwards arrow infinity of fraction numerator negative 4 x squared plus 6 x plus 4 over denominator negative x squared plus x plus 6 end fraction space times fraction numerator begin display style 1 over x squared end style over denominator begin display style 1 over x squared end style end fraction space equals limit as x rightwards arrow infinity of fraction numerator begin display style negative 4 plus 6 over x plus 4 over x squared end style over denominator begin display style negative 1 plus 1 over x plus 6 over x squared end style end fraction space space space space space space table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell bold lim with bold x bold rightwards arrow bold infinity below end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell bold C over bold x to the power of bold n end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank bold equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold 0 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold semicolon end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold italic n end table table attributes columnalign right center left columnspacing 0px end attributes row blank bold greater than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold 0 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank bold space end table space space space space space space space space space space space space space space space space space space space space space space space space space space 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 negative 4 plus 0 plus 0 over denominator negative 1 plus 0 plus 0 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 space space space 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 negative 4 over denominator negative 1 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 space space space space space space space space space space space space space space space space space space space space space space space space space space equals 4 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space$

Jadi, nilai limit di atas adalah 4