limit as x approaches+0 of 1/(csc(x))

解

x \to + 0 lim (\frac{1}{csc ( x )})

0

解答ステップ

x \to 0 lim (\frac{1}{csc ( 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} ( 1 )}{lim _{x \to 0} ( csc ( x ) )}

x \to 0 lim (1) = 1

x \to 0 lim (csc (x)) = \infty

= \frac{1}{\infty}

無限大の特性を適用する:

\frac{c}{\infty} = 0

= 0