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Chapter 2: Q 8. (page 237)
Translate expressions written in Leibniz notation to 鈥減rime鈥� notation, and vice versa.
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On earth, A falling object has a downward acceleration of 32 feet per second per second due to gravity. Suppose an object falls from an initial height of ,With an initial velocity of feet per second, Use antiderivatives to show that the equations for the position and velocity of the object after t seconds are respectively and
Differentiation review: Without using the chain rule find the derivative of each of the function f that follows some algebra may be required before differentiating
Last night Phil went jogging along Main Street. His distance from the post office t minutes after p.m. is shown in the preceding graph at the right.
(a) Give a narrative (that matches the graph) of what Phil did on his jog.
(b) Sketch a graph that represents Phil鈥檚 instantaneous velocity t minutes after p.m. Make sure you label the tick marks on the vertical axis as accurately as you can.
(c) When was Phil jogging the fastest? The slowest? When was he the farthest away from the post office? The closest to the post office?
Write down a rule for differentiating a composition of four functions
(a) in 鈥減rime鈥� notation and
(b) in Leibniz notation.
Think about what you did today and how far north you were from your house or dorm throughout the day. Sketch a graph that represents your distance north from your house or dorm over the course of the day, and explain how the graph reflects what you did today. Then sketch a graph of your velocity.
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