Pertanyaan

Nilai dari adalah ...

Nilai dari $begin mathsize 14px style limit as x rightwards arrow 2 of invisible function application open parentheses fraction numerator 2 x squared minus 6 x plus 5 over denominator x squared minus 2 x plus 1 end fraction close parentheses to the power of fraction numerator 5 x squared minus 10 x plus 5 over denominator x squared minus 4 x plus 4 end fraction end exponent end style$ adalah ...

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Perhatikan bahwa Sehingga Misalkan .Sehingga ketika x → 2 , maka n → 0 . Maka

Perhatikan bahwa

size 14px lim with size 14px n size 14px rightwards arrow size 14px 0 below size 14px invisible function application open parentheses size 14px 1 size 14px plus size 14px n close parentheses to the power of size 14px 1 over size 14px n end exponent size 14px equals size 14px e

Sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below size 14px invisible function application open parentheses fraction numerator size 14px 2 size 14px x to the power of size 14px 2 size 14px minus size 14px 6 size 14px x size 14px plus size 14px 5 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 1 end fraction close parentheses to the power of fraction numerator size 14px 5 size 14px x to the power of size 14px 2 size 14px minus size 14px 10 size 14px x size 14px plus size 14px 5 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 4 end fraction end exponent end cell row blank size 14px equals cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below size 14px invisible function application open parentheses fraction numerator size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 1 size 14px plus size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 4 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 1 end fraction close parentheses to the power of fraction numerator size 14px 5 open parentheses size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 1 close parentheses over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 4 end fraction end exponent end cell row blank size 14px equals cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below size 14px invisible function application open parentheses fraction numerator size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 1 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 1 end fraction size 14px plus fraction numerator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 4 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 1 end fraction close parentheses to the power of fraction numerator size 14px 5 open parentheses size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 1 close parentheses over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 4 end fraction end exponent end cell row blank size 14px equals cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below size 14px invisible function application open parentheses size 14px 1 size 14px plus fraction numerator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 4 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 1 end fraction close parentheses to the power of fraction numerator size 14px 5 open parentheses size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 1 close parentheses over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 4 end fraction end exponent end cell row blank size 14px equals cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below size 14px invisible function application open parentheses size 14px 1 size 14px plus open parentheses size 14px x size 14px minus size 14px 2 close parentheses to the power of size 14px 2 over open parentheses size 14px x size 14px minus size 14px 1 close parentheses to the power of size 14px 2 close parentheses to the power of fraction numerator size 14px 5 open parentheses open parentheses size 14px x size 14px minus size 14px 1 close parentheses to the power of size 14px 2 close parentheses over denominator open parentheses size 14px x size 14px minus size 14px 2 close parentheses to the power of size 14px 2 end fraction end exponent end cell row blank size 14px equals cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below size 14px invisible function application open parentheses size 14px 1 size 14px plus open parentheses size 14px x size 14px minus size 14px 2 close parentheses to the power of size 14px 2 over open parentheses size 14px x size 14px minus size 14px 1 close parentheses to the power of size 14px 2 close parentheses to the power of size 14px 5 open parentheses open parentheses size 14px x size 14px minus size 14px 1 close parentheses to the power of size 14px 2 over open parentheses size 14px x size 14px minus size 14px 2 close parentheses to the power of size 14px 2 close parentheses end exponent end cell row blank size 14px equals cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below size 14px invisible function application open parentheses size 14px 1 size 14px plus open parentheses size 14px x size 14px minus size 14px 2 close parentheses to the power of size 14px 2 over open parentheses size 14px x size 14px minus size 14px 1 close parentheses to the power of size 14px 2 close parentheses to the power of size 14px 5 open parentheses open parentheses size 14px x size 14px minus size 14px 1 close parentheses to the power of size 14px 2 over open parentheses size 14px x size 14px minus size 14px 2 close parentheses to the power of size 14px 2 close parentheses end exponent end cell row blank size 14px equals cell size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below size 14px invisible function application open parentheses size 14px 1 size 14px plus open parentheses fraction numerator size 14px x size 14px minus size 14px 2 over denominator size 14px x size 14px minus size 14px 1 end fraction close parentheses to the power of size 14px 2 close parentheses to the power of size 14px 5 open parentheses fraction numerator size 14px x size 14px minus size 14px 1 over denominator size 14px x size 14px minus size 14px 2 end fraction close parentheses to the power of size 14px 2 end exponent end cell end table$

Misalkan $size 14px n size 14px equals open parentheses fraction numerator size 14px x size 14px minus size 14px 2 over denominator size 14px x size 14px minus size 14px 1 end fraction close parentheses to the power of size 14px 2$ . Sehingga ketika x → 2 , maka n → 0 .

Maka

$size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below size 14px invisible function application open parentheses size 14px 1 size 14px plus open parentheses fraction numerator size 14px x size 14px minus size 14px 2 over denominator size 14px x size 14px minus size 14px 1 end fraction close parentheses to the power of size 14px 2 close parentheses to the power of size 14px 5 open parentheses fraction numerator size 14px x size 14px minus size 14px 1 over denominator size 14px x size 14px minus size 14px 2 end fraction close parentheses to the power of size 14px 2 end exponent size 14px equals size 14px lim with size 14px n size 14px rightwards arrow size 14px 0 below size 14px invisible function application open parentheses size 14px 1 size 14px plus size 14px n close parentheses to the power of size 14px 5 open parentheses size 14px 1 over size 14px n close parentheses end exponent size 14px equals size 14px lim with size 14px n size 14px rightwards arrow size 14px 0 below size 14px invisible function application open parentheses open parentheses size 14px 1 size 14px plus size 14px n close parentheses to the power of size 14px 1 over size 14px n end exponent close parentheses to the power of size 14px 5 size 14px equals open parentheses size 14px lim with size 14px n size 14px rightwards arrow size 14px 0 below size 14px invisible function application open parentheses size 14px 1 size 14px plus size 14px n close parentheses to the power of size 14px 1 over size 14px n end exponent close parentheses to the power of size 14px 5 size 14px equals size 14px e to the power of size 14px 5$