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

解

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

0

解答ステップ

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

cot (a) - csc (a)

の共役で乗じる

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

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

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

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

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

a \to 0 lim (1) = 1

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

= - \frac{1}{\infty}

無限大の特性を適用する:

\frac{c}{\infty} = 0

= 0