limit as x approaches 0-of x[x]cot(x)

解答

x \to 0 - lim (x [x] cot (x))

0

求解步骤

x \to 0 - lim (x [x] cot (x))

化简

x [x] cot (x) : x^{2} cot (x)

= x \to 0 - lim (x^{2} cot (x))

改写以应用洛必达法则

= x \to 0 - lim (\frac{x ^{2}}{\frac{1}{c o t ( x )}})

使用洛必达法则

= x \to 0 - lim (\frac{2 x}{sec ^{2} ( x )})

代入值

x = 0

= \frac{2 \cdot 0}{sec ^{2} ( 0 )}

化简

\frac{2 \cdot 0}{sec ^{2} ( 0 )} : 0

= 0

\frac{d}{d x} (\frac{x ^{2} + 1}{x ^{2} - 1})

\int_{0}^{1} \frac{1}{x ^{- 2}} d x

\frac{d}{d x} (x^{2} cos (\frac{1}{x}))

t^{^{'}}

\frac{\partial}{\partial x} (\frac{3 x}{4})