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

解答

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

0

求解步骤

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

乘以

cot (u) - csc (u)

的共轭根式

: \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

不定型除外

= - \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}

运用无穷大属性:

\frac{c}{\infty} = 0

= 0

x \to 0 lim ((x)^{x^{2}})

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x \to 0 lim (x ln (x^{5}))

x \to - 4 lim (\frac{1}{x - 4})

x \to 1 - lim (e^{(\frac{1}{x ^{2} - 1})})