What is the limit as x approaches 0 of (cos(4x)-1)/x ?

The limit as x approaches 0 of (cos(4x)-1)/x is 0

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limit as x approaches 0 of (cos(4x)-1)/x

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

0

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 4 sin ( 4 x )}{1})

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

Plug in the value

x = 0

= \frac{- 4 sin ( 4 \cdot 0 )}{1}

Simplify

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

= 0

\frac{\partial}{\partial y} (2 x sin (y))

v \to 4 + lim (\frac{4 - v}{∣ 4 - v ∣})

\frac{\partial}{\partial x} (x^{2} + 5)

cos^{2} (8 t)

\int_{- 1}^{1} (x^{2}) d x

What is the limit as x approaches 0 of (cos(4x)-1)/x ?
The limit as x approaches 0 of (cos(4x)-1)/x is 0