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(1) Let f be the function whose graph is shown below. 2 y = f(x) -1- 1 2 3 - 1 (a) Let g be the function defined by g(x) = f(x2 + 1). Is g continuous at 0? For full credit, you must justify your answer fully using the definition of continuity. (b) Let h be the function defined by h(x) = f(f(x)). Is h continuous at 3? For full credit, you must justify your answer fully using the definition of continuity.(2) Continuity and the Intermediate Value Theorem (a) In each part, either sketch a continuous function f(x) defined on [-4, 3] which has all three of the given properties, explain why it is impossible to do so. (i) . f(-4) = 2 (ii) . f ( -4) =2 (iii) . f( -4) = 2 . f(3) = 5 . f(3) = 5 . f(3) = -1 . f has no zeros in . f has a zero in [-4, 3] of has no zeros in [-4, 3] [-4, 3](3) Use the limit definition of the derivative to compute the derivative of f(x) = 72 . ( Work not based on the limit definition of the derivative will receive no credit.)(4) Suppose we know the following about a functionn f(x): . f(1) = 3 . f'(1) = -1 . f(9) = 1 . f' (9) = 3 (a) If g(x) = 5vx . f(x), find g'(9) (b) If h(ac) = $(20) x2+1, find h'(1)