limit as x approaches 0 of x/(csc^2(x))

解

x \to 0 lim (\frac{x}{csc ^{2} ( x )})

0

解答ステップ

x \to 0 lim (\frac{x}{csc ^{2} ( x )})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

不定形式の場合を除く

= \frac{lim _{x \to 0} ( x )}{lim _{x \to 0} ( csc ^{2} ( x ) )}

x \to 0 lim (x) = 0

x \to 0 lim (csc^{2} (x)) = \infty

= \frac{0}{\infty}

無限大の特性を適用する:

\frac{0}{\infty} = 0

= 0