Q1:

The following questions are independent of each other. (a) Suppose n(t) represents the rate at which a country's debt, in millions of dollars, is increasing where t is the number of years since 2012. Which of the following represents the increase in the country's debt between 2012 and 2019? on' (2019) On'(7) - n'(0) of 'n'(t ) at On(2019) - n(2012) (b) You walk in a straight line away from a heat source. Suppose the temperature, 7 in degrees, is a function of the distance, x in feet, from the heat source. Which of the following could be a practical interpretation of 7'(20) = -2.5 ? The temperature will be approximately o 2.50 if you are 20 feet from the heat source. 200 if you are 2.5 feet from the heat source. 2.5 colder for every 20 feet you move away from the heat source. o 2.50 colder if you move from 20 feet to 21 feet from the heat source. o 20 colder if you move 2.5 feet farther from the heat source(a) For each of the following, determine if L'Hopital's Rule applies. lim --Select--- y-2 3y - 6 Int lim -Select- 2+1 lim tan(ath) - tan(@) -Select-- h-0 h (b) Use L'Hopital's rule to evaluate the following limit. Enter your work in the answer fields below. Credit will not be given for a correct final answer without the supporting L'Hopital's rule calculation. lim 2(x - *) x -x sin(7x) lim X -*A whale is released into the ocean 100 meters due east of a coast guard station located on the shore. A camera at the coast guard station tracks the whale. If the whale swims directly away from the shore, the distance between the whale and the point of release changes and the angle 0 changes. coast guard station 100 m point of release whale Which of the following represents the relationship between the rates at which the angle, 0, and the distance between the whale and point of release, x, change? o sec2(0) dx 1 de dt 100 dt o sec-(0) de = 100 dx dt dt o tan(0)- de 1 dx = dt 100 dt o tan(0)- de x dx dt 100 dt o sec (0) do 1 dx dt 100 dt