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

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

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

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

0

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 0

x \to 0 - lim (7 (\frac{1}{x} - cot (x)))

x \to - \infty lim (- 3 x^{3} + 5)

h \to + 0 lim (\frac{h}{h ^{2} - 7 h + 1})

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

x \to 0 lim (f (x) (x^{3} - x))

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