How to find the limit of cos(2x)/x as x approaches zero [duplicate]

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Basicly the title. I know it's easy but I can't figure it out. [Edit] Not a duplicate has a 2x instead of x.

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1 Answer

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As x approaches 0 Cos(x) approaches 1 so we can in a sense think of 1/x. As x goes to 0 from the positive side 1/x approaches infinity. But when x goes to 0 from the negative side 1/x goes instead to negative infinity. This means that the limit as x goes to 0 for Cos(x)/x is undefined as the left and right limits do not agree.

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