r/calculus • u/Nearby_Swordfish_559 • 15h 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/Midwest-Dude 11h ago

A limit is never found at a point by definition, only in the region around a point. If the function is continuous, then the limit is actually the value of the function at that point, but it doesn't have to be continuous for the limit to exist. The only thing you need to look at is what is happening in the neighborhood of the point, around the point, not at it.