Pertanyaan

x → ∞ lim ( 5 − x ) ( 4 + x ) ( 3 + 7 x ) ( 5 − 2 x ) = …

$x \to \infty lim \frac{( 3 + 7 x ) ( 5 - 2 x )}{( 5 - x ) ( 4 + x )} = \dots$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari limit tersebut adalah .

nilai dari limit tersebut adalah begin mathsize 14px style 14 text end text end style

Pembahasan

Nilai dari limit tak hingga dapat dihitung dengan membagi pembilang dan penyebut dengan fungsi yang memiliki pangkat tertinggi. Jadi, nilai dari limit tersebut adalah .

Nilai dari limit tak hingga dapat dihitung dengan membagi pembilang dan penyebut dengan fungsi yang memiliki pangkat tertinggi.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator left parenthesis 3 plus 7 x right parenthesis left parenthesis 5 minus 2 x right parenthesis over denominator left parenthesis 5 minus x right parenthesis left parenthesis 4 plus x right parenthesis end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 15 minus 6 x plus 35 x minus 14 x squared over denominator 20 plus 5 x minus 4 x minus x squared end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator negative 14 x squared plus 29 x plus 15 over denominator x squared end fraction end style over denominator begin display style fraction numerator negative x squared plus x plus 20 over denominator x squared end fraction end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator negative 14 x squared over denominator x squared end fraction end style plus begin display style fraction numerator 29 x over denominator x squared end fraction end style plus begin display style 15 over x squared end style over denominator begin display style fraction numerator negative x squared over denominator x squared end fraction end style plus begin display style x over x squared end style plus begin display style 20 over x squared end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator negative 14 plus begin display style 29 over x end style plus begin display style 15 over x squared end style over denominator negative 1 plus begin display style 1 over x end style plus begin display style 20 over x squared end style end fraction end cell row blank equals cell fraction numerator negative 14 plus 0 plus 0 over denominator negative 1 plus 0 plus 0 end fraction end cell row blank equals 14 end table$

Jadi, nilai dari limit tersebut adalah begin mathsize 14px style 14 text end text end style .