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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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Final answer to the problem

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Step-by-step Solution

How should I solve this problem?

  • Solve the limit using rationalization
  • Solve using L'H么pital's rule
  • Solve without using l'H么pital
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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Apply the power rule for limits: $\lim_{x\to a}\left(f(x)\right)^n=\left(\lim_{x\to a}f(x)\right)^n$

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

Learn how to solve limits by direct substitution problems step by step online.

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

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Learn how to solve limits by direct substitution 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'H么pital'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.

Final answer to the problem

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Plotting: $\left(\frac{1-\cos\left(x\right)}{x}\right)^2$

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