A car starts from a point at 2:00 pm. and travels north at 40 mph. Another car starts from the same point at 3:00 pm. and travels west at 50 mph. After the second car has traveled i h, at what rate is the distance between the two cars changing? A spherical ball is measured to have a radius of 6 cm with a possible measurement error of i 0.1rmcm. Use the differentials to estimate the percentage error in computing the volume of the ball. A company determines a cost function of c = 6x2 180x + 2000, where c is the cost (in dollars) of producing x number of items. How many items should the company manufacture to minimize the cost? The position ofan object is given by the equation s(t) =2xz+x 6. Find the time t at which the instantaneous velocity of the object equals the average velocity in the interval [0, 3]. Question 5 10 Points Find the locations of local minimum and maximum of x9 - 4x using the second derivative test.Question 6 10 Points In a shop, the revenue and the cost of a product are determined by R (x) = 22x and C (x) =2x2+ 2x+ 1, respectively. If x represents the number of products, how many products should the shop sell to maximize the profit?Question 7 10 Points Evaluate lim by applying L'Hopital's x-0e -x-1 rule.Question 8 10 Points Let f (x) =x3 - x2- 1 and x = 1. To the nearest three decimal places, find x using Newton's 5 method of approximation.Question 9 10 Points Evaluate sin2xcos2x, dxQuestion 10 10 Points Evaluate (+2 + + + 1) dt using the - 1 Fundamental Theorem of Calculus, Part 2.Water is flowing into a tank at a rate of t r(t) :3] 3 cubic meters per minute. How much water entered the tank between 2 and 8 minutes? Question 12 10 Points To the nearest two decimal places, calculate R 5 for f (x) =x3+ 1 on [0, 4]Question 13 10 Points Use substitution to evaluate - sin2x/ 4+ 9sin -x dx. 0\fIfR denotes a region bounded above by the graph of a continuous function f(x) , below by the x-axis, and on the left and right by the lines x =a and x = b, respectively, then which of the following integrals gives the mass of the lamina with density p? Question 18 10 Points d Evaluate -cosh ( 2x2 + 1) . dxQuestion 19 10 Points - Evaluate dx . .2 1 x/ / 1+ 25Question 20 10 Points Find the vertical and horizontal asymptotes of f (x) =x+ sinx