Find the limit. lim _(xarrow 0)(1-cos(12x))/(x)= square

To find the limit of the given expression, we can use the standard trigonometric limit $\lim_{x \rightarrow 0} \frac{1 - \cos(x)}{x} = 0$. We can rewrite the given expression in a similar form by substituting $12x$ for $x$ in the standard limit.<br /><br />Let's rewrite the given expression:<br /><br />$\lim_{x \rightarrow 0} \frac{1 - \cos(12x)}{x}$<br /><br />We can rewrite this as:<br /><br />$\lim_{x \rightarrow 0} \frac{1 - \cos(12x)}{x} = 12 \cdot \lim_{x \rightarrow 0} \frac{1 - \cos(12x)}{12x}$<br /><br />Now, we can use the standard trigonometric limit $\lim_{x \rightarrow 0} \frac{1 - \cos(x)}{x} = 0$:<br /><br />$12 \cdot \lim_{x \rightarrow 0} \frac{1 - \cos(12x)}{12x} = 12 \cdot 0 = 0$<br /><br />Therefore, the limit of the given expression is 0.