limit as x approaches 0 of (3-3cos(x))/(sin^2(x))

解答

x \to 0 lim (\frac{3 - 3 cos ( x )}{sin ^{2} ( x )})

\frac{3}{2}

十进制

1.5

求解步骤

x \to 0 lim (\frac{3 - 3 cos ( x )}{sin ^{2} ( x )})

使用洛必达法则

= x \to 0 lim (\frac{3 sin ( x )}{sin ( 2 x )})

使用洛必达法则

= x \to 0 lim (\frac{3 cos ( x )}{cos ( 2 x ) \cdot 2})

代入值

x = 0

= \frac{3 cos ( 0 )}{cos ( 2 \cdot 0 ) \cdot 2}

化简

\frac{3 cos ( 0 )}{cos ( 2 \cdot 0 ) \cdot 2} : \frac{3}{2}

= \frac{3}{2}

d er i v a t i v e f (x) = \frac{11}{( 1 - x ) ^{2}}

\int sin^{3} (2 x) d x

f^{^{''}} (x) = x^{- \frac{3}{2}}

\int x 4 - x d x

\int cos^{3} (x) sin (x) d x