Find the limit of $\left(\frac{1-\cos\left(x\right)}{x}\right)^2$ as $x$ approaches 0

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${\left(\lim_{x\to0}\left(\frac{1-\cos\left(x\right)}{x}\right)\right)}^2$

Learn how to solve problems step by step online. Find the limit of ((1-cos(x))/x)^2 as x approaches 0. Apply the power rule for limits: \lim_{x\to a}\left(f(x)\right)^n=\left(\lim_{x\to a}f(x)\right)^n. If we directly evaluate the limit \lim_{x\to 0}\left(\frac{1-\cos\left(x\right)}{x}\right) as x tends to 0, we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately. After deriving both the numerator and denominator, the limit results in.