Nilai x→0lim​3x−tan(2x)sin(7x)​=…

Pertanyaan

Nilai limit as x rightwards arrow 0 of fraction numerator sin open parentheses 7 x close parentheses over denominator 3 x minus tan open parentheses 2 x close parentheses end fraction equals horizontal ellipsis space

  1. negative 7 over 3 space

  2. negative 7 over 2 space

  3. 7 over 3 space

  4. 1 space

  5. 7 space

B. Hamdani

Master Teacher

Mahasiswa/Alumni Universitas Airlangga

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Substitusi langsung:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator sin open parentheses 7 x close parentheses over denominator 3 x minus tan open parentheses 2 x close parentheses end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator sin open parentheses 0 close parentheses over denominator 0 minus tan open parentheses 0 close parentheses end fraction end cell row blank equals cell 0 over 0 space left parenthesis tak space tentu right parenthesis end cell end table

Mengubah fungsi trigonometri:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 0 of fraction numerator sin open parentheses 7 x close parentheses over denominator 3 x minus tan open parentheses 2 x close parentheses end fraction end cell equals cell limit as x rightwards arrow 0 of fraction numerator sin open parentheses 7 x close parentheses over denominator 3 x minus tan open parentheses 2 x close parentheses end fraction cross times fraction numerator begin display style 1 over x end style over denominator begin display style 1 over x end style end fraction end cell row blank equals cell limit as x rightwards arrow 0 of fraction numerator begin display style fraction numerator sin open parentheses 7 x close parentheses over denominator x end fraction end style over denominator begin display style fraction numerator 3 x over denominator x end fraction end style minus begin display style fraction numerator tan open parentheses 2 x close parentheses over denominator x end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style limit as x rightwards arrow 0 of fraction numerator sin open parentheses 7 x close parentheses over denominator x end fraction end style over denominator begin display style limit as x rightwards arrow 0 of fraction numerator 3 x over denominator x end fraction minus limit as x rightwards arrow 0 of fraction numerator tan open parentheses 2 x close parentheses over denominator x end fraction end style end fraction end cell row blank equals cell fraction numerator 7 over denominator 3 minus 2 end fraction end cell row blank equals 7 end table 

Oleh karena itu, jawaban yang benar adalah E.

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