Question: Q5. Solve the following questions: (a) Use the intermediate value theorem to prove that the equation V/9 - 4x2 + 4x = 1 + arccos(x)

Q5. Solve the following questions: (a) Use the intermediate value theorem

Q5. Solve the following questions: (a) Use the intermediate value theorem to prove that the equation V/9 - 4x2 + 4x = 1 + arccos(x) has a solution in (-1, 0). [8 marks] (b) lim 125 sin (-) [8 marks] x40 1 - cos(2) f (2x) - f(2(x - h)) (c) Assume that lim f(x th) - f(I) = cos(2r?) for all r, find lim (You are h-0 h h-+0 h not allowed to use L'Hopital's rule in evaluating this limit). (8 marks]

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