Pertanyaan

x → ∞ lim 98 + 9 9 x − 1 + 10 0 x + 3 9 9 x − 10 0 x + 1 + 98 = … + 3 m u .

$x \to \infty lim \frac{9 9 ^{x} - 10 0 ^{x + 1} + 98}{98 + 9 9 ^{x - 1} + 10 0 ^{x + 3}} = \dots + 3 m u .$

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G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

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$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of invisible function application fraction numerator 99 to the power of x minus 100 to the power of x plus 1 end exponent plus 98 over denominator 98 plus 99 to the power of x minus 1 end exponent plus 100 to the power of x plus 3 end exponent end fraction end cell equals cell limit as x rightwards arrow infinity of invisible function application fraction numerator 99 to the power of x minus 100 to the power of x plus 1 end exponent plus 98 over denominator 98 plus 99 to the power of x minus 1 end exponent plus 100 to the power of x plus 3 end exponent end fraction times fraction numerator 1 over 100 to the power of x over denominator 1 over 100 to the power of x end fraction end cell row blank equals cell limit as x rightwards arrow infinity of invisible function application fraction numerator open parentheses 99 over 100 close parentheses to the power of x minus 100 plus 98 over 100 to the power of x over denominator 98 over 100 to the power of x plus 1 over 99 open parentheses 99 over 100 close parentheses to the power of x plus 1000000 end fraction end cell row blank equals cell fraction numerator 0 minus 100 plus 0 over denominator 0 plus 0 plus 1000000 end fraction end cell row blank equals cell negative 1 over 10000 end cell end table end style$

Maka $begin mathsize 14px style limit as x rightwards arrow infinity of invisible function application fraction numerator 99 to the power of x minus 100 to the power of x plus 1 end exponent plus 98 over denominator 98 plus 99 to the power of x minus 1 end exponent plus 100 to the power of x plus 3 end exponent end fraction equals negative 1 over 10000 end style$

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