A curve has the equation y = h(x)

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Presentation transcript:

A curve has the equation y = h(x) A curve has the equation y = h(x). Choose an expression for the slope of the secant line through the points P(2, h(2)) and Q(x, h(x)) from the following: 1. {image} 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The displacement (in meters) of a particle moving in a straight line is given by the equation of motion {image} , which is measured in seconds. Find the velocity of the particle at t = 3. Choose the correct answer from the following: 244 250 252 255 242 245 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

If an arrow is shot upward on the moon with a velocity of 54 m/s its height (in meters) after t seconds is given by {image} . When will the arrow hit the moon? Round the result to the nearest thousandth if necessary. Choose the correct answer from the following: 92.525 91.514 91.526 91.525 91.53 91.415 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Consider the slope of the given curve at each of the five points shown Consider the slope of the given curve at each of the five points shown.List these five slopes in decreasing order . {applet} V, X, L, C, K V, L, X, K, C C, K, L, V, X X, V, L, K, C 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

If a cylindrical tank holds 100,000 gallons of water, which can be drained from the bottom of the tank in an hour, then Torricelli's Law gives the volume of water remaining in the tank after t minutes as {image} . Find the rate at which the water is flowing out of the tank (the instantaneous rate of change of V with respect to t) as a function of t. Choose the correct answer from the following: 1. {image} 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50