What is the limit as x approaches 0 of (1-cos(2x))/(10x^2) ?

The limit as x approaches 0 of (1-cos(2x))/(10x^2) is 1/5

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limit as x approaches 0 of (1-cos(2x))/(10x^2)

x \to 0 lim (\frac{1 - cos ( 2 x )}{10 x ^{2}})

\frac{1}{5}

Decimal

0.2

Solution steps

x \to 0 lim (\frac{1 - cos ( 2 x )}{10 x ^{2}})

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

= \frac{1}{10} \cdot x \to 0 lim (\frac{1 - cos ( 2 x )}{x ^{2}})

Apply L'Hopital's Rule

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

= \frac{1}{10} \cdot x \to 0 lim (\frac{2 sin ( 2 x )}{2 x})

Apply L'Hopital's Rule

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

= \frac{1}{10} \cdot x \to 0 lim (\frac{4 cos ( 2 x )}{2})

Plug in the value

x = 0

= \frac{1}{10} \cdot \frac{4 cos ( 2 \cdot 0 )}{2}

Simplify

\frac{1}{10} \cdot \frac{4 cos ( 2 \cdot 0 )}{2} : \frac{1}{5}

= \frac{1}{5}

x \to 0 + lim (304)

x \to - 4 lim ((6 x - 2) (4 x - 5))

x \to 0 + lim (x \cdot ln (x^{2}))

x \to 4 lim (- 12 x^{2} + 72 x - 60)

n \to 0 lim (\frac{n}{n + 1})

What is the limit as x approaches 0 of (1-cos(2x))/(10x^2) ?
The limit as x approaches 0 of (1-cos(2x))/(10x^2) is 1/5