t→0lim​tan tsin t−t​=....

Pertanyaan

limit as straight t rightwards arrow 0 of fraction numerator sin space straight t minus straight t over denominator tan space straight t end fraction equals....

  1. negative 2

  2. negative 1

  3. 0

  4. 1

  5. 2

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Jawaban yang benar dari pertanyaan tersebut adalah C.

Perhatikan beberapa sifat pada limit berikut : 

  • limit as x rightwards arrow 0 of space f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis equals limit as x rightwards arrow 0 of space f left parenthesis x right parenthesis space minus space limit as x rightwards arrow 0 of space g left parenthesis x right parenthesis
  • limit as straight x rightwards arrow 0 of space space fraction numerator sin space ax over denominator tan space bx end fraction equals limit as straight x rightwards arrow 0 of space fraction numerator ax over denominator tan space bx end fraction equals straight a over straight b

Sehingga soal dapat diselesaikan seperti berikut :

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as straight t rightwards arrow 0 of fraction numerator sin space straight t minus straight t over denominator tan space straight t end fraction end cell equals cell limit as t rightwards arrow 0 of space fraction numerator sin space t over denominator tan space t end fraction minus fraction numerator t over denominator tan space t end fraction end cell row blank equals cell limit as t rightwards arrow 0 of space fraction numerator sin space t over denominator tan space t end fraction minus limit as t rightwards arrow 0 of space fraction numerator t over denominator tan space t end fraction end cell row blank equals cell 1 minus 1 end cell row blank equals 0 end table

Oleh karena itu, jawaban yang benar adalah C.

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