limit as t approaches 0 of (sin(-3t))/t

解答

t \to 0 lim (\frac{sin ( - 3 t )}{t})

- 3

求解步骤

t \to 0 lim (\frac{sin ( - 3 t )}{t})

使用洛必达法则

= t \to 0 lim (\frac{- cos ( 3 t ) \cdot 3}{1})

代入值

t = 0

= \frac{- cos ( 3 \cdot 0 ) \cdot 3}{1}

化简

\frac{- cos ( 3 \cdot 0 ) \cdot 3}{1} : - 3

= - 3

x \to 0 - lim (x^{2} \cdot ln (- x))

x \to 0 lim ((\frac{1}{x}) (\frac{1}{3} - \frac{1}{x + 9}))

x \to 1 lim (\frac{x - 1}{2})

x \to \frac{π}{3} - lim (sin (3 x))

x \to - 1 lim (2 x - 2)