Pertanyaan

Nilai dari adalah ...

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

M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

Misalkan , sehingga . Ketika , maka . Sehingga

Misalkan , sehingga . Ketika , maka .

Sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight infinity of invisible function application x sin invisible function application open parentheses fraction numerator 1 over denominator 2 x end fraction close parentheses end cell equals cell limit as x rightwards arrow straight infinity of invisible function application x sin invisible function application 1 half open parentheses 1 over x close parentheses end cell row blank equals cell limit as y rightwards arrow 0 of invisible function application 1 over y sin invisible function application 1 half y end cell row blank equals cell limit as y rightwards arrow 0 of invisible function application fraction numerator sin invisible function application 1 half y over denominator y end fraction end cell row blank equals cell limit as y rightwards arrow 0 of invisible function application open parentheses fraction numerator sin invisible function application 1 half y over denominator y end fraction times fraction numerator 1 half over denominator 1 half end fraction close parentheses end cell row blank equals cell limit as y rightwards arrow 0 of invisible function application open parentheses fraction numerator sin invisible function application 1 half y over denominator 1 half y end fraction times 1 half close parentheses end cell row blank equals cell 1 times 1 half end cell row blank equals cell 1 half end cell end table end style$