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Question Number 175122 by Michaelfaraday last updated on 20/Aug/22

Answered by Ar Brandon last updated on 20/Aug/22

$$\mathcal{L}=\underset{x\to 0}{\lim }\frac{1-\sqrt[2022]{\cos \left(2021x\right)}}{x^2}$$$$=\underset{x\to 0}{\lim }\frac{1-{(1-\frac{{2021}^2{x}^2}{2})}^{\frac{1}{2022}}}{x^2}$$$$=\underset{x\to 0}{\lim }\frac{1}{x^2}(1-(1-\frac{{2021}^2{x}^2}{4044}))=\frac{{2021}^2}{4044}$$

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