limit as θ approaches 0 of (sin(3θ))/(2θ)

解答

θ \to 0 lim (\frac{sin ( 3 θ )}{2 θ})

\frac{3}{2}

十进制

1.5

求解步骤

θ \to 0 lim (\frac{sin ( 3 θ )}{2 θ})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{2} \cdot θ \to 0 lim (\frac{sin ( 3 θ )}{θ})

使用洛必达法则

= \frac{1}{2} \cdot θ \to 0 lim (\frac{cos ( 3 θ ) \cdot 3}{1})

代入值

θ = 0

= \frac{1}{2} \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1}

化简

\frac{1}{2} \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1} : \frac{3}{2}

= \frac{3}{2}

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