Constant acceleration due to gravity

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Write down their equations, if any. (b) Let g : (0, co) —> IR be de?ned by g(a: )—(i) How many asymptotes has g( )?83:E SE(i i) How many asymptotes has 9 ( )1? Write down their equations, if any. (iii) What IS the range of g (2:)? [9 marks]4. Consider the expression2v 3:2(a) Specify a suitable domain to make f a valid function.(b) Express the range of f in Set notation, given the above domain.[4 marks] 5. With all quantities expressed in suitable units of measurement, the speed v of a body of mass mfalling through the air under gravity near the earth’s surface can be expressed as a function of timet by the formula where g > U is the constant acceleration due to gravity and k > 0 is a constant value that measuresthe effect of air resistance. (a) Show that the body will eventually reach a limiting speed (known as terminal velocity).(b) Taking k = 0.1 and g = 10, determine the terminal velocity for a falling body of mass 1 unit.(c) Using the values in part (b), sketch the graph of v(t) for t E [0, 100].

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