limit as x approaches 0 of (2sin(x)-sin(2x))/(sin(x)-xcos(x))

解答

x \to 0 lim (\frac{2 sin ( x ) - sin ( 2 x )}{sin ( x ) - x cos ( x )})

3

求解步骤

x \to 0 lim (\frac{2 sin ( x ) - sin ( 2 x )}{sin ( x ) - x cos ( x )})

使用洛必达法则

= x \to 0 lim (\frac{2 cos ( x ) - cos ( 2 x ) \cdot 2}{x sin ( x )})

使用洛必达法则

= x \to 0 lim (\frac{- 2 sin ( x ) + 4 sin ( 2 x )}{sin ( x ) + x cos ( x )})

使用洛必达法则

= x \to 0 lim (\frac{- 2 cos ( x ) + 8 cos ( 2 x )}{2 cos ( x ) - x sin ( x )})

代入值

x = 0

= \frac{- 2 cos ( 0 ) + 8 cos ( 2 \cdot 0 )}{2 cos ( 0 ) - 0 \cdot sin ( 0 )}

化简

\frac{- 2 cos ( 0 ) + 8 cos ( 2 \cdot 0 )}{2 cos ( 0 ) - 0 \cdot sin ( 0 )} : 3

= 3

\int_{0}^{4} 3 t^{4} + 3 t + 2 d t

n = 0 \sum \infty (\frac{x}{3})^{n}

\frac{\partial}{\partial x} (e^{3 x yz - 7})

n = 1 \sum \infty n (\frac{5}{3})^{n}

t a y l or z^{i}