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

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##  Step-by-step Solution 

Problem to solve:

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

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Apply the power rule for limits: $\lim_{x\to a}\left(f(x)\right)^n=\left(\lim_{x\to a}f(x)\right)^n$

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

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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.

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##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Limits by Direct SubstitutionLimits by L'Hôpital's ruleLimits by factoringLimits by rationalizing

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