Pertanyaan

Nilai dari x → ∞ lim ( 3 x + 1 ) 2 ( 2 x − 3 ) ( 5 − 4 x ) adalah ....

Nilai dari $x \to \infty lim \frac{( 2 x - 3 ) ( 5 - 4 x )}{( 3 x + 1 ) ^{2}}$ adalah ....

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari $limit as x rightwards arrow infinity of fraction numerator open parentheses 2 x minus 3 close parentheses open parentheses 5 minus 4 x close parentheses over denominator open parentheses 3 x plus 1 close parentheses squared end fraction$ adalah negative 8 over 9

Pembahasan

Bagi dengan pangkat tertinggi untuk setiap pembilang dan penyebutnya, Jadi, nilai dari adalah .

Bagi dengan pangkat tertinggi open parentheses x squared close parentheses untuk setiap pembilang dan penyebutnya,

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of fraction numerator open parentheses 2 x minus 3 close parentheses open parentheses 5 minus 4 x close parentheses over denominator open parentheses 3 x plus 1 close parentheses squared end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 10 x minus 8 x squared minus 15 plus 12 x over denominator 9 x squared plus 6 x plus 1 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator negative 8 x squared plus 22 x minus 15 over denominator 9 x squared plus 6 x plus 1 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator negative 8 up diagonal strike x squared end strike over denominator up diagonal strike x squared end strike end fraction end style plus begin display style fraction numerator 22 up diagonal strike x over denominator x to the power of up diagonal strike 2 end exponent end fraction end style minus begin display style 15 over x squared end style over denominator begin display style fraction numerator 9 up diagonal strike x squared end strike over denominator up diagonal strike x squared end strike end fraction end style plus begin display style fraction numerator 6 up diagonal strike x over denominator x to the power of up diagonal strike 2 end exponent end fraction end style plus begin display style 1 over x squared end style end fraction end cell row blank equals cell fraction numerator negative 8 plus 0 minus 0 over denominator 9 plus 0 plus 0 end fraction end cell row blank equals cell negative 8 over 9 end cell end table$

Jadi, nilai dari $limit as x rightwards arrow infinity of fraction numerator open parentheses 2 x minus 3 close parentheses open parentheses 5 minus 4 x close parentheses over denominator open parentheses 3 x plus 1 close parentheses squared end fraction$ adalah negative 8 over 9 .