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 ( - 0 ) ) \cdot 4}{1}

Simplify

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

= 4

x \to \frac{1}{2} + lim (\frac{4}{2 x - 1})

x \to 3 lim ((3 - x) ln (x - 3))

x \to 0 + lim (x ln (8 x))

x \to 2 lim (- \frac{∣ x - 2 ∣}{x - 2})

x \to 4 lim (2 x^{2} - 3 x + 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