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Step-by-step Solution

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

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Answer

$\frac{1}{2}$$\,\,\left(Decimal: 0.5\right)$

Step-by-step explanation

Problem to solve:

$\lim_{x\to 0}\left(\frac{1-\cos\left(x\right)}{x^2}\right)$
1

As the limit results in indeterminate form, we can apply L'Hôpital's rule

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

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Answer

$\frac{1}{2}$$\,\,\left(Decimal: 0.5\right)$
$\lim_{x\to 0}\left(\frac{1-\cos\left(x\right)}{x^2}\right)$

Main topic:

Limits

Related formulas:

7. See formulas

Time to solve it:

~ 0.12 seconds

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