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Nilai dari adalah ...

Nilai dari $begin mathsize 14px style limit as x rightwards arrow 2 of invisible function application open parentheses fraction numerator negative 2 x plus 7 over denominator x squared minus 2 x plus 3 end fraction close parentheses to the power of fraction numerator 2 x squared minus 4 x plus 6 over denominator x squared minus 4 end fraction end exponent end style$ adalah ...

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

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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 minus size 14px n close parentheses to the power of size 14px 1 over size 14px n end exponent size 14px equals size 14px e to the power of size 14px minus size 14px 1 end exponent

Sehingga

$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 minus size 14px 2 size 14px x size 14px plus size 14px 7 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 3 end fraction close parentheses to the power of fraction numerator size 14px 2 size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 6 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 end fraction end exponent size 14px equals 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 3 size 14px minus size 14px x to the power of size 14px 2 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 3 end fraction close parentheses to the power of fraction numerator size 14px 2 size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 6 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 end fraction end exponent size 14px equals size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below size 14px invisible function application open parentheses fraction numerator 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 3 close parentheses size 14px minus open parentheses size 14px x to the power of size 14px 2 size 14px minus size 14px 4 close parentheses 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 3 end fraction close parentheses to the power of fraction numerator size 14px 2 size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 6 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 end fraction end exponent size 14px equals 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 3 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 3 end fraction size 14px minus fraction numerator size 14px x to the power of size 14px 2 size 14px minus 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 3 end fraction close parentheses to the power of fraction numerator size 14px 2 size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 6 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 end fraction end exponent size 14px equals 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 minus fraction numerator size 14px x to the power of size 14px 2 size 14px minus 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 3 end fraction close parentheses to the power of fraction numerator size 14px 2 size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 6 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 end fraction end exponent size 14px equals 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 minus fraction numerator size 14px x to the power of size 14px 2 size 14px minus 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 3 end fraction close parentheses to the power of fraction numerator size 14px 2 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 3 close parentheses over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 end fraction end exponent size 14px equals 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 minus fraction numerator size 14px x to the power of size 14px 2 size 14px minus 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 3 end fraction close parentheses to the power of size 14px 2 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 3 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 end fraction close parentheses end exponent$

Misalkan $size 14px n size 14px equals fraction numerator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 3 end fraction size 14px comma$ Sehingga ketika x → 2, maka n → 0.

Maka

$size 14px lim with size 14px x size 14px rightwards arrow size 14px 2 below size 14px invisible function application open parentheses size 14px 1 size 14px minus fraction numerator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 3 end fraction close parentheses to the power of size 14px 2 open parentheses fraction numerator size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 3 over denominator size 14px x to the power of size 14px 2 size 14px minus size 14px 4 end fraction close parentheses end exponent size 14px equals size 14px lim with size 14px n size 14px rightwards arrow size 14px 0 below size 14px invisible function application open parentheses size 14px 1 size 14px minus size 14px n close parentheses to the power of size 14px 2 open parentheses size 14px 1 over size 14px n close parentheses end exponent size 14px equals size 14px lim with size 14px n size 14px rightwards arrow size 14px 0 below size 14px invisible function application open parentheses open parentheses size 14px 1 size 14px minus size 14px n close parentheses to the power of size 14px 1 over size 14px n end exponent close parentheses to the power of size 14px 2 size 14px equals open parentheses size 14px lim with size 14px n size 14px rightwards arrow size 14px 0 below size 14px invisible function application open parentheses size 14px 1 size 14px minus size 14px n close parentheses to the power of size 14px 1 over size 14px n end exponent close parentheses to the power of size 14px 2 size 14px equals open parentheses size 14px e to the power of size 14px minus size 14px 1 end exponent close parentheses to the power of size 14px 2$