Pertanyaan

Nilai dari x → ∞ lim ( x 2 cos 2 x 1 − x 2 ) adalah...

Nilai dari $x \to \infty lim (x^{2} cos^{2} \frac{1}{x} - x^{2})$ adalah...

2
1
0
-1
-2

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Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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Pembahasan

Misalkan , , sehingga bentuk di atas menjadi:

$limit as straight x rightwards arrow infinity of straight x squared open parentheses cos squared 1 over straight x minus 1 close parentheses equals limit as straight y rightwards arrow 0 of 1 over straight y squared open parentheses cos squared straight y minus 1 close parentheses equals limit as straight y rightwards arrow 0 of 1 over straight y squared open parentheses negative sin squared space straight y close parentheses equals negative limit as straight y rightwards arrow 0 of fraction numerator sin squared space straight y over denominator straight y squared end fraction equals negative limit as straight y rightwards arrow 0 of open parentheses fraction numerator sin space straight y over denominator straight y end fraction close parentheses squared equals negative open parentheses limit as straight y rightwards arrow 0 of fraction numerator sin space straight y over denominator straight y end fraction close parentheses squared equals negative open parentheses 1 over 1 close parentheses squared equals negative 1$