Answer 1 and 2

handwritten then box the final answers

A woman standing on a cliff is watching a motor boat through a telescope as the boat approaches the shoreline directly below her. If the telescope is 250 feet above the water level and if the boat is approaching the cliff at 20 ft/s, at what rate is the acute angle made by the telescope with the vertical changing when the boat is 250 feet from the shore? 2 Use differentials to approximate the increase in the surface area of a soap bubble when its radius increases from 3 inches to 3.025 inches. 31 ) Let f ( x ) = Inx a ) Find the local liner approximation of of at 40= 1 b) Use the previous item to approximate In (0.92) Use local linear approximation to estimate (2.001) 5 S .) Use local linear approximation to estimate e 0.01 + 0.01 In 1.02 A company is known for producing high quality calculators. The price-demand function for selling r calculators is given by p(x) = 412 -60r, while the profit in selling r is determined by P(x) = 3x3 - 54x2 + 15x - 150. Determine the number of calculators that must be sold in order to minimize cost. A manufacturer determines that the profit derived from selling x units of a certain 7 . ) item is given by P(x) = 0.0002x3 + 10x pesos What is the profit earned in selling the 51st unit