# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Choose the solving method

Learn how to solve definite integrals problems step by step online.

$\frac{0}{0}$

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

$\lim_{x\to0}\left(\frac{\sin\left(x\right)}{2x}\right)$$\,\,\left(\approx 0.5\right)$
$\lim_{x\to0}\frac{1-\cos\left(x\right)}{x^2}$

### Main topic:

Definite Integrals

### Time to solve it:

~ 0.06 s (SnapXam)