Pertanyaan

Nilai dari adalah ...

Nilai dari $begin mathsize 14px style limit as x rightwards arrow straight infinity of invisible function application fraction numerator tan squared invisible function application open parentheses 4 over x close parentheses over denominator 3 over x squared end fraction end style$ adalah ...

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H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Misalkan , maka . Ketika , maka . Sehingga

Misalkan , maka . Ketika , maka .

Sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight infinity of invisible function application fraction numerator tan squared invisible function application open parentheses 4 over x close parentheses over denominator 3 over x squared end fraction end cell equals cell limit as x rightwards arrow straight infinity of invisible function application fraction numerator tan squared invisible function application open parentheses 4 times 1 over x close parentheses over denominator 3 times 1 over x times 1 over x end fraction end cell row blank equals cell limit as y rightwards arrow 0 of invisible function application fraction numerator tan squared invisible function application 4 y over denominator 3 times y times y end fraction end cell row blank equals cell limit as y rightwards arrow 0 of invisible function application fraction numerator tan invisible function application 4 y times tan invisible function application 4 y over denominator 3 times y times y end fraction end cell row blank equals cell limit as y rightwards arrow 0 of invisible function application open parentheses 1 third times fraction numerator tan invisible function application 4 y over denominator y end fraction times fraction numerator tan invisible function application 4 y over denominator y end fraction close parentheses end cell row blank equals cell limit as y rightwards arrow 0 of invisible function application open parentheses 1 third times fraction numerator tan invisible function application 4 y over denominator y end fraction times 4 over 4 times fraction numerator tan invisible function application 4 y over denominator y end fraction times 4 over 4 close parentheses end cell row blank equals cell limit as y rightwards arrow 0 of invisible function application open parentheses 1 third times fraction numerator tan invisible function application 4 y over denominator 4 y end fraction times 4 times fraction numerator tan invisible function application 4 y over denominator 4 y end fraction times 4 close parentheses end cell row blank equals cell 1 third times 1 times 4 times 1 times 4 end cell row blank equals cell 16 over 3 end cell end table end style$