What is the limit as x approaches 0 of (cos(2x)-1)/x ?

The limit as x approaches 0 of (cos(2x)-1)/x is 0

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limit as x approaches 0 of (cos(2x)-1)/x

x \to 0 lim (\frac{cos ( 2 x ) - 1}{x})

0

Solution steps

x \to 0 lim (\frac{cos ( 2 x ) - 1}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 2 sin ( 2 x )}{1})

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

Plug in the value

x = 0

= \frac{- 2 sin ( 2 \cdot 0 )}{1}

Simplify

\frac{- 2 sin ( 2 \cdot 0 )}{1} : 0

= 0

\int \frac{25}{x} d x

\int 16 t + sec^{2} (t) d t

\frac{d}{d x} (\frac{( x ^{5} + 3 x ) ^{4}}{cos ( x )})

9 y \frac{d y}{d x} - 4 x = 0

\frac{d}{d x} (\frac{3}{( 8 x + 3 ) ^{2}})

What is the limit as x approaches 0 of (cos(2x)-1)/x ?
The limit as x approaches 0 of (cos(2x)-1)/x is 0