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MATH 171, PRACTICE TEST 3 Q1. Find the antiderivatives of √ x x, x3 + 1 √ x Q2. Find the area under y = x2 from x = 1 to x = 3 using Riemann sums. Q3. Find the critical numbers for f (x) = 2x3 − 9x2 + 12x + 2 and classify them as local max or min. Q4. Find the maximum and minimum values of f (x) = x−1 x2 on [1, 3]. Q5. Find the critical point of ex cos x in [0, π/2] and decide whether it is a local max or min. Q6. Find the minimum value of f (x) = 2x3/2 − 3x on [0, ∞). Q7. Find the area under one arch of y = sin x. Q8. A circular can with top is to be made with a fixed surface area S. Find the dimensions that give the maximum volume. Q9. Find the antiderivative of 1 x2 + 2x + ex + . 3 x 1 + x2 Q10. A ball is dropped from the top of a cliff and hits the ground 2 seconds later. How high was the cliff?