What is the limit as x approaches 0 of (6sin(2x))/x ?

The limit as x approaches 0 of (6sin(2x))/x is 12

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limit as x approaches 0 of (6sin(2x))/x

x \to 0 lim (\frac{6 sin ( 2 x )}{x})

12

Solution steps

x \to 0 lim (\frac{6 sin ( 2 x )}{x})

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

= 6 \cdot x \to 0 lim (\frac{sin ( 2 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 2 x ) \cdot 2}{1})

= 6 \cdot x \to 0 lim (\frac{cos ( 2 x ) \cdot 2}{1})

Plug in the value

x = 0

= 6 \cdot \frac{cos ( 2 \cdot 0 ) \cdot 2}{1}

Simplify

6 \cdot \frac{cos ( 2 \cdot 0 ) \cdot 2}{1} : 12

= 12

(2, - 14), (1, - 11)

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What is the limit as x approaches 0 of (6sin(2x))/x ?
The limit as x approaches 0 of (6sin(2x))/x is 12