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Pertanyaan

Hitunglah nilai limit fungsi limit as x rightwards arrow 0 of fraction numerator sin space x over denominator sin space 2 x end fraction

R. Azizatul

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

nilai limit fungsi tersebut adalah 1 half.

Pembahasan

Limit fungsi trigonometri di atas dapat diselesaikan dengan mengalikan dengan x over x dan fraction numerator 2 x over denominator 2 x end fractionsebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator sin space x over denominator sin space 2 x end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator sin space x over denominator sin space 2 x end fraction times x over x times fraction numerator 2 x over denominator 2 x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator sin space x over denominator x end fraction times limit as x rightwards arrow 0 of fraction numerator 2 x over denominator sin space 2 x end fraction times fraction numerator x over denominator 2 x end fraction end cell row blank equals cell open parentheses 1 close parentheses times open parentheses 1 close parentheses times open parentheses 1 half close parentheses end cell row blank equals cell 1 half end cell end table 

Dengan demikian, nilai limit fungsi tersebut adalah 1 half.

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