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Please help with the following questions 1. Carefully justify all your answers. (a) Suppose that lim f(I) exists. Does this imply that f(a) is defined?

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Please help with the following questions

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1. Carefully justify all your answers. (a) Suppose that lim f(I) exists. Does this imply that f(a) is defined? What condition ensures that f(a) is defined? (2 marks) (b) State the Extreme Value Theorem. (3 marks] (c) State Fermat's Theorem. [2 marks) (d) Using first principles, prove that the derivative of any constant function is zero. (3 marks]

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