limit as u approaches 0 of cot(u)-csc(u)

解

u \to 0 lim (cot (u) - csc (u))

0

解答ステップ

u \to 0 lim (cot (u) - csc (u))

cot (u) - csc (u)

の共役で乗じる

\frac{- 1}{cot ( u ) + csc ( u )}

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

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 _{u \to 0} ( 1 )}{lim _{u \to 0} ( cot ( u ) + csc ( u ) )}

u \to 0 lim (1) = 1

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

= - \frac{1}{\infty}

無限大の特性を適用する:

\frac{c}{\infty} = 0

= 0