Q.

By Posted on

materi : Limit

lim = frac{ {2}^{x + 1} - {3}^{x - 2} + {4}^{x + 2} }{ {2}^{x - 2} + {3}^{x + 1} + {4}^{x - 1} } = \
x → ∞

ayo para ahli mtk :
@Henriyulianto
@Sinogen
Bang kelvin (@kelvinho) entah username agak sulit:v
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Yooooooo belajar Biologi lagi ke bang @jn245 nanti:)​

Q.

Jawab:

64

PEMBAHASAN

Limit

begin{aligned}Biggl.&lim_{xtoinfty}:frac{ 2^{x+1} - 3^{x-2} + 4^{x+2} }{ 2^{x-2} + 3^{x+1} + 4^{x-1} }\Biggl.{= }&lim_{xtoinfty}:frac{ 2^{x+1} - 3^{x-2} + 2^{2x+4} }{ 2^{x-2} + 3^{x+1} + 2^{2x-2} }divfrac{2^{2x-2}}{2^{2x-2}}\Biggl.{= }&lim_{xtoinfty}:frac{ 2^{-x+3} - dfrac{3^{x-2}}{2^{2x-2}} + 2^{6} }{ 2^{-x} + dfrac{3^{x+1}}{2^{2x-2}} + 1 }\Bigl.&quadleft[ textsf{dengan pengecualian pada bentuk tak tentu} right.end{aligned}

begin{aligned}Biggl.{= }&frac{limlimits_{xtoinfty}:2^{-x+3} - dfrac{3^{x-2}}{2^{2x-2}} + 2^{6}}{limlimits_{xtoinfty}:2^{-x} + dfrac{3^{x+1}}{2^{2x-2}} + 1}\Biggl.{= }&frac{limlimits_{xtoinfty}:dfrac{8}{2^x} - limlimits_{xtoinfty}:dfrac{3^{x-2}}{2^{2x-2}} + limlimits_{xtoinfty}:2^{6}}{limlimits_{xtoinfty}:dfrac{1}{2^x} + limlimits_{xtoinfty}:dfrac{3^{x+1}}{2^{2x-2}} + limlimits_{xtoinfty}:1}end{aligned}

begin{aligned}Biggl.{= }&frac{0-0+2^6}{0+0+1} = 2^6\Bigl.{= }&boxed{ bf64 }end{aligned}