Let f be defined by f (x) = | 1 − x2 | a) Sketch the graph of f. b) Prove that f is continuous at x = 1. c) Determine if f is derivable at x = 1. Justify.

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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.