Pertanyaan

Nilai dari x → ∞ lim ( 2 x 3 − 8 x + 5 ) 2 ( 3 x 2 − 7 x + 4 ) 3 = ...

Nilai dari $x \to \infty lim \frac{( 3 x ^{2} - 7 x + 4 ) ^{3}}{( 2 x ^{3} - 8 x + 5 ) ^{2}} = ...$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai limitnya adalah .

nilai limitnya adalah begin mathsize 14px style 27 over 4 end style

Pembahasan

Ingat: . Jadi, nilai limitnya adalah .

Ingat: limit as x rightwards arrow infinity of k over x to the power of n equals k over infinity to the power of n equals 0 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses 3 x squared minus 7 x plus 4 close parentheses cubed over open parentheses 2 x cubed minus 8 x plus 5 close parentheses squared end cell equals cell limit as x rightwards arrow infinity of fraction numerator open parentheses 3 x squared close parentheses cubed plus... plus 4 cubed over denominator open parentheses 2 x cubed close parentheses squared plus... plus 5 squared end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 27 x to the power of 6 plus... plus 64 over denominator 4 x to the power of 6 plus... plus 25 end fraction cross times fraction numerator begin display style 1 over x to the power of 6 end style over denominator begin display style 1 over x to the power of 6 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator 27 x to the power of 6 over denominator x to the power of 6 end fraction end style plus... plus begin display style 64 over x to the power of 6 end style over denominator begin display style fraction numerator 4 x to the power of 6 over denominator x to the power of 6 end fraction end style plus... plus begin display style 25 over x to the power of 6 end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 27 plus... plus 64 over x to the power of 6 end style over denominator begin display style 4 plus... plus 25 over x to the power of 6 end style end fraction end cell row blank equals cell fraction numerator begin display style 27 plus... plus 0 end style over denominator begin display style 4 plus... plus 0 end style end fraction end cell row blank equals cell 27 over 4 end cell end table$

Jadi, nilai limitnya adalah .