Pertanyaan

Nilai x → 0 lim sin x + sin 3 x 4 x cos x = ....

Nilai $x \to 0 lim \frac{4 x cos x}{sin x + sin 3 x}$ = ....

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Klaim

S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style limit as straight x rightwards arrow 0 of invisible function application space fraction numerator 4 straight x space cos space invisible function application straight x over denominator sin invisible function application space straight x plus sin space invisible function application 3 straight x end fraction equals limit as straight x rightwards arrow 0 of invisible function application space fraction numerator 4 straight x straight space. straight space cos invisible function application space straight x over denominator 2 space sin space invisible function application 1 half open parentheses straight x plus 3 straight x close parentheses space cos invisible function application space 1 half open parentheses straight x minus 3 straight x close parentheses end fraction equals limit as straight x rightwards arrow 0 of invisible function application space fraction numerator 2 straight x. cos space invisible function application straight x over denominator sin invisible function application space 2 straight x. space cos space invisible function application left parenthesis negative straight x right parenthesis end fraction equals limit as straight x rightwards arrow 0 of invisible function application space fraction numerator 2 straight x. cos space invisible function application straight x over denominator sin invisible function application space 2 straight x. space cos space invisible function application straight x end fraction equals limit as straight x rightwards arrow 0 of invisible function application space fraction numerator 2 straight x over denominator sin invisible function application space 2 straight x end fraction equals 2 over 2 equals 1 end style$