What is the limit as x approaches 0 of (sin(4x))/((2x)) ?

The limit as x approaches 0 of (sin(4x))/((2x)) is 2

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limit as x approaches 0 of (sin(4x))/((2x))

x \to 0 lim (\frac{sin ( 4 x )}{( 2 x )})

2

Solution steps

x \to 0 lim (\frac{sin ( 4 x )}{2 x})

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

= \frac{1}{2} \cdot x \to 0 lim (\frac{sin ( 4 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 4 x ) \cdot 4}{1})

= \frac{1}{2} \cdot x \to 0 lim (\frac{cos ( 4 x ) \cdot 4}{1})

Plug in the value

x = 0

= \frac{1}{2} \cdot \frac{cos ( 4 \cdot 0 ) \cdot 4}{1}

Simplify

\frac{1}{2} \cdot \frac{cos ( 4 \cdot 0 ) \cdot 4}{1} : 2

= 2

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What is the limit as x approaches 0 of (sin(4x))/((2x)) ?
The limit as x approaches 0 of (sin(4x))/((2x)) is 2