Pertanyaan

Nilai dari adalah ...

Nilai dari $begin mathsize 14px style limit as x rightwards arrow 3 of invisible function application open parentheses 10 minus x squared close parentheses to the power of fraction numerator 3 over denominator open parentheses x squared minus 9 close parentheses end fraction end exponent end style$ adalah ...

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Klaim

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa Sehingga Misalkan . Sehingga ketika x → 3 , 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 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

$size 14px lim with size 14px x size 14px rightwards arrow size 14px 3 below size 14px invisible function application open parentheses size 14px 10 size 14px minus size 14px x to the power of size 14px 2 close parentheses to the power of fraction numerator size 14px 3 over denominator open parentheses size 14px x to the power of size 14px 2 size 14px minus size 14px 9 close parentheses end fraction end exponent size 14px equals size 14px lim with size 14px x size 14px rightwards arrow size 14px 3 below size 14px invisible function application open parentheses size 14px 1 size 14px plus size 14px 9 size 14px minus size 14px x to the power of size 14px 2 close parentheses to the power of fraction numerator size 14px 3 over denominator open parentheses size 14px x to the power of size 14px 2 size 14px minus size 14px 9 close parentheses end fraction end exponent size 14px equals size 14px lim with size 14px x size 14px rightwards arrow size 14px 3 below size 14px invisible function application open parentheses size 14px 1 size 14px minus size 14px x to the power of size 14px 2 size 14px plus size 14px 9 close parentheses to the power of fraction numerator size 14px 3 over denominator open parentheses size 14px x to the power of size 14px 2 size 14px minus size 14px 9 close parentheses end fraction end exponent size 14px equals size 14px lim with size 14px x size 14px rightwards arrow size 14px 3 below size 14px invisible function application open parentheses size 14px 1 size 14px minus open parentheses size 14px x to the power of size 14px 2 size 14px minus size 14px 9 close parentheses close parentheses to the power of fraction numerator size 14px 3 over denominator open parentheses size 14px x to the power of size 14px 2 size 14px minus size 14px 9 close parentheses end fraction end exponent$

Misalkan . Sehingga ketika x → 3 , maka n → 0.

Maka

$size 14px lim with size 14px x size 14px rightwards arrow size 14px 3 below size 14px invisible function application open parentheses size 14px 1 size 14px minus open parentheses size 14px x to the power of size 14px 2 size 14px minus size 14px 9 close parentheses close parentheses to the power of fraction numerator size 14px 3 over denominator open parentheses size 14px x to the power of size 14px 2 size 14px minus size 14px 9 close parentheses end fraction end exponent size 14px equals size 14px lim with size 14px n size 14px rightwards arrow size 14px 0 below size 14px invisible function application open parentheses size 14px 1 size 14px minus size 14px n close parentheses to the power of size 14px 3 over size 14px n end exponent size 14px equals size 14px lim with size 14px n size 14px rightwards arrow size 14px 0 below size 14px invisible function application open parentheses open parentheses size 14px 1 size 14px minus size 14px n close parentheses to the power of size 14px 1 over size 14px n end exponent close parentheses to the power of size 14px 3 size 14px equals open parentheses size 14px lim with size 14px n size 14px rightwards arrow size 14px 0 below size 14px invisible function application open parentheses size 14px 1 size 14px minus size 14px n close parentheses to the power of size 14px 1 over size 14px n end exponent close parentheses to the power of size 14px 3 size 14px equals open parentheses size 14px e to the power of size 14px minus size 14px 1 end exponent close parentheses to the power of size 14px 3 size 14px equals size 14px e to the power of size 14px minus size 14px 3 end exponent$