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

解

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

0

解答ステップ

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

cot (b) - csc (b)

の共役で乗じる

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

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

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

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

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

b \to 0 lim (1) = 1

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

= - \frac{1}{\infty}

無限大の特性を適用する:

\frac{c}{\infty} = 0

= 0