limit as x approaches 0+of csc(x)-cot(x)

解

x \to 0 + lim (csc (x) - cot (x))

0

解答ステップ

x \to 0 + lim (csc (x) - cot (x))

csc (x) - cot (x)

の共役で乗じる

\frac{1}{csc ( x ) + cot ( x )}

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

x \to 0 + lim (1) = 1

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

= \frac{1}{\infty}

無限大の特性を適用する:

\frac{c}{\infty} = 0

= 0