1. Graph of f The function f is defined on the closed interval [-2, 6]. The graph of f consists of two quarter-circles and three lines segments, as shown above. Let g be the function defined by g(x) = f(t) dt. a) Determine all values of x, besides x = 2, on the interval -2 sxs6 for which g(x) = 0. Justify your answer. b) For each of g(3), g '(3) and g "(3), find the value or state for which it does not exist. c) On what open interval(s) contained in -2

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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.