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

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

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

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

0

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{5 sin ( 5 x )}{1})

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

Plug in the value

x = 0

= \frac{5 sin ( 5 \cdot 0 )}{1}

Simplify

\frac{5 sin ( 5 \cdot 0 )}{1} : 0

= 0

\int sin (π x) sin (nπ x) d x

\frac{d}{d x} (x^{3} \cdot ln (x))

y = y

\frac{k x}{a ^{2} + x ^{2}}

f (x) = x (x - 2), at x = 1

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