Question 1 47 / 50 pts Consider the region A in the first quadrant bounded by the graphs of f (x) = and g (a ) = sin( 3 a Find the area of the region b) Find the slope of the tangent line to the graph of g (@) = sin 3 at the point where f (x ) and g (@) intersect.Question 2 27K 50 pts Noxious gas is naturally produced in an underground cavern at the rate of 'i'T T (t) 6605(10 liters per hour at timet hours,t E 0. The initial amount of gas that is in the cavern at t : 0 is 10 liters. At time t : 10 hours, a pump begins to remove the noxious gas at a rate of 2 liters per hour. b) What is the total amount of gas in the cavern at time t = 10 hours? c) What is the absolute maximum amount of gas in the cavern over the time interval [10, 20] hours? Justify your answer. Question 1 0 f 6 Pts Find the area of the region bounded by the graph of y2 = 1 3: and the yaxis. When you solve for y, you will have only the top half of the curve. So when you integrate on [0, 2], make sure you double your integral. Question 6 0 ' 6 \"ts Find the volume generated by rotating about the x-axis the area bounded by m) =4mm2 andy= at. '2'\":- (KJ ' This problem requires the washer method. Find R and r by taking "top curve bottom curve" where the bottom curve is the x-axis. When you integrate, don't forget the constant 7r. The limits of integration come from the intersection points of the two curves. m Question 7 0/6pt5 .1322? n l i: {2 {'l l 3 fly :r l '3 (all: )2 11' air; 2 3 2 71" 1 (QB _ 2) d3: where the right curve is the line x=2. Which of the following integrals represents the volume of the solid formed by revolving the region bounded bvyr : :33 ,y : 1 , and a: : 2 about the line Graph the region. Since the region is adjacent to the axis of revolution, this problem requires the disk method. To nd r, take "right curve left curve"