Pertanyaan

Nilai dari adalah ....

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

12
- 12

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H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

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Pembahasan

Misalkan , maka . Sehingga ketika , maka . Maka

Misalkan , maka .

Sehingga ketika , maka .

Maka

$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 csc invisible function application open parentheses 4 over x close parentheses over denominator 3 x end fraction end cell equals cell limit as x rightwards arrow straight infinity of invisible function application open parentheses fraction numerator 1 over denominator 3 x end fraction times csc invisible function application 4 open parentheses 1 over x close parentheses close parentheses end cell row blank equals cell limit as x rightwards arrow straight infinity of invisible function application open parentheses 1 third times 1 over x times csc invisible function application 4 open parentheses 1 over x close parentheses close parentheses end cell row blank equals cell limit as y rightwards arrow 0 of invisible function application open parentheses 1 third times y times csc invisible function application 4 y close parentheses end cell row blank equals cell limit as y rightwards arrow 0 of invisible function application open parentheses 1 third times y times fraction numerator 1 over denominator sin invisible function application 4 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 y over denominator sin invisible function application 4 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 y over denominator sin invisible function application 4 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 4 y over denominator sin invisible function application 4 y end fraction times 1 fourth close parentheses end cell row blank equals cell 1 third times 1 times 1 fourth end cell row blank equals cell 1 over 12 end cell end table end style$

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