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Nilai dari adalah ...

Nilai dari $begin mathsize 14px style limit as x rightwards arrow straight infinity of invisible function application fraction numerator cos invisible function application open parentheses 2 over x close parentheses minus 1 over denominator 1 minus cos squared invisible function application open parentheses 3 over x close parentheses end fraction end style$ adalah ...

H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa Sehingga Misalkan . Ketiks , maka . Sehingga

Perhatikan bahwa

Sehingga

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Misalkan . Ketiks , maka .

Sehingga

$begin mathsize 14px style negative 2 times open parentheses limit as x rightwards arrow straight infinity of invisible function application fraction numerator sin invisible function application open parentheses 1 over x close parentheses over denominator sin invisible function application 3 open parentheses 1 over x close parentheses end fraction close parentheses squared equals negative 2 times open parentheses limit as y rightwards arrow 0 of invisible function application fraction numerator sin invisible function application y over denominator sin invisible function application 3 y end fraction close parentheses squared equals negative 2 times open parentheses limit as y rightwards arrow 0 of invisible function application open parentheses fraction numerator sin invisible function application y over denominator sin invisible function application 3 y end fraction times fraction numerator 3 y over denominator 3 y end fraction close parentheses close parentheses squared equals negative 2 times open parentheses limit as y rightwards arrow 0 of invisible function application open parentheses fraction numerator sin invisible function application y over denominator y end fraction times fraction numerator 3 y over denominator sin invisible function application 3 y end fraction times 1 third close parentheses close parentheses squared equals negative 2 times open parentheses 1 times 1 times 1 third close parentheses squared equals negative 2 times open parentheses 1 third close parentheses squared equals negative 2 times 1 over 9 equals negative 2 over 9 end style$