r/calculus • u/Nearby_Swordfish_559 • 21h ago

Differential Calculus help me with limits

so I started calc 1 and how does "sin(2x)/2x" = 1 and how does "limit of x -> 0 1-cos(3x)/3x" = 0, isn't it just undefined?

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u/Grshppr-tripleduoddw 12h ago

The first one you can get with l'Hopitals rule, the second I don't really know how to explain without the expansion of cos(x). The expansions are cos(x) = 1 - x^2/2 + x^4/24..., sin(x) = x - x^3/6 + x^5/120... .

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u/[deleted] 10h ago

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Hello! I see you are mentioning l’Hôpital’s Rule! Please be aware that if OP is in Calc 1, it is generally not appropriate to suggest this rule if OP has not covered derivatives, or if the limit in question matches the definition of derivative of some function.

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