Pertanyaan

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

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

S. Lestari

Master Teacher

Jawaban terverifikasi

Jawaban

limit as x rightwards arrow infinity of open parentheses 4 x minus 3 close parentheses squared over open parentheses 2 x plus 5 close parentheses squared equals 4

Pembahasan

Ingat bahwa Maka dapat diperoleh Jadi,

Ingat bahwa

limit as x rightwards arrow infinity of 1 over x to the power of n equals 0 comma space n greater than 0

Maka dapat diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of open parentheses 4 x minus 3 close parentheses squared over open parentheses 2 x plus 5 close parentheses squared end cell equals cell limit as x rightwards arrow infinity of fraction numerator 16 x squared minus 24 x plus 9 over denominator 4 x squared plus 20 x plus 25 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator x squared open parentheses 16 minus begin display style 24 over x end style plus begin display style 9 over x squared end style close parentheses over denominator x squared open parentheses 4 plus begin display style 20 over x end style plus begin display style 25 over x squared end style close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 16 minus begin display style 24 over x end style plus begin display style 9 over x squared end style over denominator 4 plus begin display style 20 over x end style plus begin display style 25 over x squared end style end fraction end cell row blank equals cell fraction numerator 16 minus 0 plus 0 over denominator 4 plus 0 plus 0 end fraction end cell row blank equals 4 end table$

Jadi, limit as x rightwards arrow infinity of open parentheses 4 x minus 3 close parentheses squared over open parentheses 2 x plus 5 close parentheses squared equals 4