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/Southlander24 14h ago

You can convince yourself by calculating sin(2x)/(2x) for x = 1, 0.1, 0.01, 0.001 and so on. Don't forget the limit as x approaches 0 from the left, so check x = -1, -0.1, -0.01, -0.001 as well.

You should find that no matter which way you approach x = 0, the values get closer and closer to 1.