w06e - Math 151 Workshop 6 1 At time t = 0 Irwin fires a...

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Unformatted text preview: Math 151, Workshop 6 1. At time t = 0, Irwin fires a rubber band at a spider on the ceiling. At time t = 3 the rubber band hits the spider and then the rubber band falls. Suppose s(t) represents the height of the rubber band above the floor at time t. a) Which is larger, s(1) or s(2)? b) Which is larger, s (1) or s (2)? c) Sketch possible graphs of s and s for 0 t 4. 2. An object moves along the s-axis, with displacement s = s(t) (meters), velocity v = v(t) (m/sec) and acceleration a = a(t) (m/sec2 ). It so happens that the velocity and displacement are related by the equation v = 8s + 16. Moreover, at the instant t = 0, the object is observed at s = 6. a) Show that a is constant, and find its value. b) Graph v as a function of s. c) Graph v as a function of t. 3. Values of a twice differentiable function, f , and its first and second derivatives are in the table to the right. Use this information to answer the following questions as well as you can. a) If g(x) = f (x) , compute g(2), g (2), and g (2). b) If h(x) = f (x2 ), compute h(2), h (2), and h (2). c) If k(x) = f (f (x)), compute k(2), k (2), and k (2). d) If h is a small number, write an approximation (the linearization of f at 3) for f (3 + h). 4. Differentiate the following functions: a) f (x) = cos2 (x3 ). b) f (x) = ln(cos5 (3x4 )). c) f (x) = ln(ln(ln(sec x))). d) f (x) = tan cot(7x). 2 x 1 2 3 4 f (x) 2 3 7 2 f (x) f (x) 0 2 6 5 3 -4 5 7 e) f (x) = 10(1 + (2 - (6 + (7x4 )9 )3 )5 . ...
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