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

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

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

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

4

Solution steps

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})

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

Plug in the value

x = 0

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

Simplify

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

= 4

\frac{d}{d x} (A cos (2 x))

\int sin (nπ x) d x

\frac{d}{d x} ((x + 1) (x + 3))

\frac{( x + 1 )}{( 5 - x )}

t \to 1 lim (\frac{\frac{1}{t}}{t - 1})

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