1. Consider the trigonometric function f(t) =
(a) What is the amplitude of f(t)?
(b) What is the period of f(t)?
(c) What are the maximum and minimum values attained by f(t)?
(d) Sketch the graph of f(t) for t ε [¡6; 6].
2. At rest, the human heart beats once every second. At the strongest part of the beat, a person's blood pressure peaks at 120mmHg. At the most relaxed part of the beat, a person's blood pressure drops to 80mmHg. Supposing that t = 0 corresponds to the peak of the beat, write down a trigonometric function that captures this behaviour. Sketch the blood pressure over two heart beats.
3. The volume of grains in a silo at a particular time (measured in hours) is given by V (t) = 4t(3 - t) m3 . Find the rate of change of the volume of grains in the silo from first principles (using the de¯nition of the rate of change).
4. Consider the function f(x) = 2x2 + 1. Find the equation of the tangent to the graph of f(x) at x = 2. [NOTE: when calculating f'(0)
(2), use first principles.]
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