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

解答

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

4

求解步骤

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

使用洛必达法则

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

使用洛必达法则

= x \to 0 lim (\frac{- cos ( x ) + 9 cos ( 3 x )}{2})

代入值

x = 0

= \frac{- cos ( 0 ) + 9 cos ( 3 \cdot 0 )}{2}

化简

\frac{- cos ( 0 ) + 9 cos ( 3 \cdot 0 )}{2} : 4

= 4

x \to 1 + lim (ln (x) \cdot ln (x - 1))

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

x \to 1 lim (sin (x - 1))

x \to 4 lim (3 x + 2)

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