Pertanyaan

x → ∞ lim x cot ( x 1 ) sin ( x 2 1 ) = .....

$x \to \infty lim x cot (\frac{1}{x}) sin (\frac{1}{x ^{2}}) =$ .....

-2
-1
0
1
2

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A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style limit as straight x rightwards arrow straight infinity of invisible function application space straight x space cot space invisible function application open parentheses 1 over straight x close parentheses space sin space invisible function application open parentheses 1 over straight x squared close parentheses Misalkan straight u equals 1 over straight x space maka space straight x equals 1 over straight u space dan space 1 over straight x squared equals straight u squared Untuk space straight x rightwards arrow infinity space maka space straight u rightwards arrow 0 limit as straight u rightwards arrow 0 of invisible function application space 1 over straight u space cot space invisible function application straight u. space sin space invisible function application straight u squared limit as straight u rightwards arrow 0 of space invisible function application fraction numerator sin space invisible function application straight u squared over denominator straight u. tan space invisible function application straight u end fraction equals 1 end style$