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

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## Step-by-step Solution

Problem to solve:

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

Choose the solving method

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If we directly evaluate the limit $\lim_{x\to 0}\left(\frac{1-2\cos\left(x\right)+\cos\left(x\right)^2}{1-\cos\left(x\right)}\right)$ as $x$ tends to $0$, we can see that it gives us an indeterminate form

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Learn how to solve limits problems step by step online.

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Learn how to solve limits problems step by step online. Find the limit of (1-2cos(x)cos(x)^2)/(1-cos(x)) as x approaches 0. If we directly evaluate the limit \lim_{x\to 0}\left(\frac{1-2\cos\left(x\right)+\cos\left(x\right)^2}{1-\cos\left(x\right)}\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. If we directly evaluate the limit \lim_{x\to 0}\left(\frac{2\sin\left(x\right)-\sin\left(2x\right)}{\sin\left(x\right)}\right) as x tends to 0, we can see that it gives us an indeterminate form.

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

Limits

~ 0.13 s