Step-by-step Solution

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

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Step-by-step explanation

Problem to solve:

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

Learn how to solve limits problems step by step online.

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

Unlock this full step-by-step solution!

Learn how to solve limits problems step by step online. Evaluate the limit of (x^2)/(1-cos(x)) as x approaches 0. If we try to evaluate the limit directly, it results in indeterminate form. Then we need to apply L'Hôpital's rule. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a sum of two functions is the sum of the derivatives of each function. The derivative of the constant function (1) is equal to zero.

Final Answer

$2$

Problem Analysis

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

Main topic:

Limits

Related formulas:

7. See formulas

Time to solve it:

~ 0.06 seconds