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Let arctan x - x COS X if x > 0 f (x) = 3x3 + 11x2 -4x if x SO 2 + 3x -

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Let arctan x - x COS X if x > 0 f (x) = 3x3 + 11x2 -4x if x SO 2 + 3x - 4 whenever it's defined. (a) (9 points) Find the domain of f and justify that f is continuous. (b) (5 points) Discuss whether there is an extension of f which is continuous over R. (c) (6 points) Find the horizontal/oblique asymptotes of the graph of f, if any

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