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

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

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

x \to 0 lim (\frac{1 - cos ( x )}{5 x ^{2}})

\frac{1}{10}

Decimal

0.1

Solution steps

x \to 0 lim (\frac{1 - cos ( x )}{5 x ^{2}})

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

= \frac{1}{5} \cdot x \to 0 lim (\frac{1 - cos ( x )}{x ^{2}})

Apply L'Hopital's Rule

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

= \frac{1}{5} \cdot x \to 0 lim (\frac{sin ( x )}{2 x})

Apply L'Hopital's Rule

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

= \frac{1}{5} \cdot x \to 0 lim (\frac{cos ( x )}{2})

Plug in the value

x = 0

= \frac{1}{5} \cdot \frac{cos ( 0 )}{2}

Simplify

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

= \frac{1}{10}

y^{^{'}} - y = 10 t e^{2 t}

\int \frac{1}{y ^{2} + 1} d y

\frac{d}{d x} (e^{y} + \frac{y}{x})

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

\frac{d}{d x} (arcsin (8 x) + arccos (8 x))

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