Exercise 1: A particle moves according to a law of motion s = fit), where t 20, t (seconds) and s (feet). (a) Find the velocity at time t. (b) When is the particle at rest? (c) When is the particle moving in the positive direction? (d) Find the total distance traveled during the first 5 seconds. f (t) =+3 -912 + 24t (@) When is the particle speeding up? Slowing down? Exercise 2: A water tank has the shape of an inverted circular cone with base radius 3 m and height 5 m. If water is being pumped into the tank at a rate of 3 m/min, find the rate at which the water level is rising when the water is 4 m deep. Exercise 3: (a) Find the differential dy. I+1 [b) Evaluate dy when x = 2, dx = 0.05. I- 1 Exorcise 4: Find the absolute maximum and the absolute minimum values of the function f (x) = 2x - 3x - 12x + 1, [-2, 3] . Exercise 5: Show that the equation has exactly one real root: 2r - 1 - sinr = 0. Exorcise 6: Find the limit or show that it doesn't exist: VI + 3x2 lim I-+-00 4x - 1 Exorcise 7: Use the guidelines of sketching a curve to sketch the curve Exercice & A box with square base and open top must have a volume of 32,000 cm. Find the dimensions of the box that minimize the amount of material used. Exercise 9: Find the most general antiderivative of the function f (x) = 3Vr - 2VI. Exercise 10: (extra credit) A stone is thrown upward with a speed of 50 ft's from the edge of a cliff 450 ft above the ground: (a) Find the height of the stone above the ground t seconds later. (b) When does it reach its maximum height? (c) When does it strike the ground