calculus3a-s: Problem 3 (5 points) The circumference of a sphere was measured to be 83.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface area.calculus3a-s: Problem 4 (5 points) You are wondering how inaccuracies in the radius or height of your can effect the volume of the can. Use differentials to answer the questions below. An error of p percent in the radius will cause an error of approximately percent in the volume of the can. An error of p percent in the height will cause an error of approximately percent in the volume of the can. Note that although the sentences above contain the word "approximately", the answers are actually determined precisely by the procedure with which we compute them. For example for the dependence on the radius you consider h constant, and you use the differentials dV = V'(r)dr. The percentage of the error in v is 100dV V and you know that 100dr P= and dV = dV dr dr. Your answer will depend on p. Proceed similarly for the dependence of the error on h.calculus3a-s: Problem 5 (5 points) N E W- Suppose a police officer is 1/2 mile south of an intersection, driving north towards the intersection at 35 mph. At the same time, another car is 1/2 mile east of the intersection, driving east (away from the intersection) at an unknown speed. The officer's radar gun indicates 15 mph when pointed at the other car (that is, the straight-line distance between the officer and the other car is increasing at a rate of 15 mph). What is the speed of the other car? Speed = mph Now suppose that the officer's radar gun indicates -15 mph instead (that is, the straight-line distance is decreasing at a rate of 15 mph). What is the speed of the other car this time? Speed = mphcalculus3a-s: Problem 6 (5 points) A price p (in dollars) and demand _ for a product are related by 2x2 - 6xp + 50p- = 7000. If the price is increasing at a rate of 2 dollars per month when the price is 10 dollars, find the rate of change of the demand Rate of change of demand =calculus3a-s: Problem 7 (5 points) Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 8 cubic feet per minute. If the pool has radius 3 feet and height 12 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 8 feet? (Include help (units) with your answer.)