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Math 1210-1 Final Practice 3 1. Evaluate 4 X 1 i=2 2. Simplify n X i . (2i + 1)(3i − 1) such that there is no sigma notation in your result. i=1 3. Suppose 6 X i=2 Z 4. Suppose ai = 3 and 6 X bi = 6. Evaluate i=2 f (x) dx = 3 and 2 (2ai − bi + 1). i=2 Z 6 6 X Z 6 g(x) dx = 6. Evaluate 2 6 (2f (x) − g(x) + 1) dx. 2 5. Suppose f (x) = x5 − 4x3 − 3x + 1. Evaluate f (2) and f (3). What can you conclude about the solution(s) of f (x) = 0. √ 3 6. Suppose f (x) = x2 defined on the interval [−1, 27/8]. Find the average slope of f (x) on [−1, 27/8]. Find all real numbers c such that f 0 (c) equals to the average slope. Why there is no c inside the interval [−1, 27/8]? √ 3 7. Suppose f (x) = x2 defined on the interval [−1, 8]. Find the average value of f (x) on [−1, 8]. Find a real number c between −1 and 8 such that f (c) equals to the average value.