Prove that ', 12 and lº norms satisfy the properties (N1)-(N3). (N1) (Positivity) ||x|| > 0, and ||x || = 0 +x = 0 (N2) (Homogeneity) ||ax || = |a| ||x || for all a E R (N3) (Triangle inequality) ||æ + y || < ||æ || + ||Y ||

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.