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Question Number 205138 by Thokna last updated on 10/Mar/24

$$A=\underset{x\to 0}{\lim }\frac{1-\cos 2x}{2x^2}$$$$=\underset{x\to 0}{\lim }\frac{{2\sin }^{2}x}{2x^2}$$$$=\underset{x\to 0}{\lim }{\left(\frac{\sin x}{x}\right)}^2=1$$$$B=\underset{x\to 0}{\lim }\frac{1}{x\cot x}$$$$=\underset{x\to 0}{\lim }\frac{\tan x}{x}=\underset{x\to 0}{\lim }\frac{\sin x}{x}\times \frac{1}{\cos x}=1$$

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