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

The limit as x approaches 0 of (2sin(4x))/x is 8

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

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

8

Solution steps

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

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

= 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})

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

Plug in the value

x = 0

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

Simplify

2 \cdot \frac{cos ( 4 \cdot 0 ) \cdot 4}{1} : 8

= 8

x \to 0 + lim ((x) (ln (x)))

x \to 0 + lim (ln (e^{x} - 1))

x \to + 0 lim (\frac{( cos ( m x ) - cos ( n x ) )}{x ^{2}})

x \to 0 lim (4 x - 8)

x \to \frac{1}{2} + lim (x^{2} tan (π x))

What is the limit as x approaches 0 of (2sin(4x))/x ?
The limit as x approaches 0 of (2sin(4x))/x is 8