limit as x approaches 0 of (cos(2x)-cos(5x))/(x^2)

解答

x \to 0 lim (\frac{cos ( 2 x ) - cos ( 5 x )}{x ^{2}})

\frac{21}{2}

十进制

10.5

求解步骤

x \to 0 lim (\frac{cos ( 2 x ) - cos ( 5 x )}{x ^{2}})

使用洛必达法则

= x \to 0 lim (\frac{- 2 sin ( 2 x ) + 5 sin ( 5 x )}{2 x})

使用洛必达法则

= x \to 0 lim (\frac{- 4 cos ( 2 x ) + 25 cos ( 5 x )}{2})

代入值

x = 0

= \frac{- 4 cos ( 2 \cdot 0 ) + 25 cos ( 5 \cdot 0 )}{2}

- 4 cos (2 \cdot 0) + 25 cos (5 \cdot 0) = 21

= \frac{21}{2}

\int e^{5 x} cos (3 x) d x

\int cos (2 x) - sin (\frac{x}{2}) d x

l a pl a ce t r an s f or m t \cdot sin (k \cdot t)

x \to - 4 lim (- 5 x - 8)

x y^{^{'}} - 2 y = x^{2} - x - 2