Pertanyaan

Nilai dari x → ∞ lim x tan ( 2 x 1 ) adalah ...

Nilai dari $x \to \infty lim x tan (\frac{1}{2 x})$ adalah ...

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A. Khairunisa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Misal , sehingga . Ketika , maka . Sehingga

Misal begin mathsize 14px style straight y equals 1 over straight x end style , sehingga . Ketika , maka .

Sehingga

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