limit as x approaches pi/2 of (2x-pi)tan(x)

解答

x \to \frac{π}{2} lim ((2 x - π) tan (x))

- 2

求解步骤

x \to \frac{π}{2} lim ((2 x - π) tan (x))

改写以应用洛必达法则

= x \to \frac{π}{2} lim (\frac{- π + 2 x}{\frac{1}{t a n ( x )}})

使用洛必达法则

= x \to \frac{π}{2} lim (\frac{2}{- csc ^{2} ( x )})

代入值

x = \frac{π}{2}

= \frac{2}{- csc ^{2} ( \frac{π}{2} )}

化简

\frac{2}{- csc ^{2} ( \frac{π}{2} )} : - 2

= - 2

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x \to 4 lim (\frac{2 x - 4}{x - 1})

x \to - \infty lim (- (x)^{2})

x \to 3 - lim (\frac{x}{9 - x ^{2}})

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