What is the limit as x approaches 0 of (20sin(3x))/x ?

The limit as x approaches 0 of (20sin(3x))/x is 60

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limit as x approaches 0 of (20sin(3x))/x

x \to 0 lim (\frac{20 sin ( 3 x )}{x})

60

Solution steps

x \to 0 lim (\frac{20 sin ( 3 x )}{x})

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

= 20 \cdot x \to 0 lim (\frac{sin ( 3 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{1})

= 20 \cdot x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{1})

Plug in the value

x = 0

= 20 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1}

Simplify

20 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1} : 60

= 60

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What is the limit as x approaches 0 of (20sin(3x))/x ?
The limit as x approaches 0 of (20sin(3x))/x is 60