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Nilai dari x → ∞ lim 2 x + 3 − 9 2 x + 11 = ⋯

Nilai dari $x \to \infty lim \frac{2 ^{x} + 11}{2 ^{x + 3} - 9} = \dots$

M. Robo

Master Teacher

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Ingat kembali bahwa : dan Bagi dengan pangkat tertingginya :

Ingat kembali bahwa :

begin mathsize 14px style bold lim with bold x bold rightwards arrow bold infinity below bold 1 over bold x bold equals bold 0 end style

dan

begin mathsize 14px style bold lim with bold x bold rightwards arrow bold infinity below bold 1 over bold k to the power of bold x bold equals bold 0 end style

Bagi dengan pangkat tertingginya begin mathsize 14px style left parenthesis 2 to the power of straight x plus 3 end exponent right parenthesis end style :

$begin mathsize 14px style equals limit as straight x rightwards arrow infinity of fraction numerator 2 to the power of straight x plus 11 over denominator 2 to the power of straight x plus 3 end exponent minus 9 end fraction space. space open parentheses fraction numerator begin display style 1 over 2 to the power of straight x plus 3 end exponent end style over denominator begin display style 1 over 2 to the power of straight x plus 3 end exponent end style end fraction close parentheses equals limit as straight x rightwards arrow infinity of fraction numerator begin display style 2 to the power of straight x over 2 to the power of straight x plus 3 end exponent end style plus begin display style 11 over 2 to the power of straight x plus 3 end exponent end style over denominator begin display style 2 to the power of straight x plus 3 end exponent over 2 to the power of straight x plus 3 end exponent end style minus begin display style 9 over 2 to the power of straight x plus 3 end exponent end style end fraction equals limit as straight x rightwards arrow infinity of fraction numerator 2 to the power of straight x minus left parenthesis straight x plus 3 right parenthesis end exponent plus begin display style 11 over 2 to the power of straight x plus 3 end exponent end style over denominator 2 to the power of straight x plus 3 minus left parenthesis straight x plus 3 right parenthesis end exponent minus begin display style 9 over 3 to the power of straight x plus 3 end exponent end style end fraction equals limit as straight x rightwards arrow infinity of fraction numerator 2 to the power of negative 3 end exponent plus begin display style 11 over 2 to the power of straight x plus 3 end exponent end style over denominator 2 to the power of 0 minus begin display style 9 over 2 to the power of straight x plus 3 end exponent end style end fraction equals fraction numerator begin display style 1 over 8 end style plus 0 over denominator 1 minus 0 end fraction equals 1 over 8 end style$