f(x) = e* at x = 1 (a) Find the differential dy for function f. dy = ex dx (b) Evaluate dy and Ay at the given value of x when (i) Be sure to provide your answers to three decimal places. If the Ax = 0.5, (ii) Ax = 0.1, and (iii) Ax = 0.01. answer is less than one, include the leading zero, e.g. 0.nnn (i) dy ~ (i) Ay ~ (ii) dy ~ (ii) Ay ~ (iii) dy ~ (iii) Ay ~ (c) Find the error |Ay - dyl for each choice of dx = Ax. Be sure to provide your answer to three decimal places. If the answer is less than one, include the leading zero, e.g. 0.nnn(c) Find the error | Ay - dyl for each choice of dx = Ax. Be sure to provide your answer to three decimal places. If the answer is less than one, include the leading zero, e.g. 0.nnn (i) (ii) (iii)A circular plate is heated and expands. If the radius of the plate increases from R = 10 cm to R = 10.1 cm, use differentials to approximate the increase in the area of the top surface. Enter your answer in terms of it. To find the height of a building, the length of the shadow of a 3 meter pole placed 9 m from the building is measured. See the figure. This measurement is found to be 1 m, with a percentage error of 1%. The height of the building is estimated to be 30 m. Use differentials to find the percentage error in the estimate. Round your answer to one decimal height place. 3 m 9m-The radius of a spherical ball is found by measuring the volume of the sphere (by nding how much water it displaces). It is determined that the volume is 40 cubic centimeters (cm3), with a tolerance of no more than 1%. (a) Use differentials to approximate the relative error in measuring the radius. Enter your answer as a fraction. Themem no moreman xw (b) Find the corresponding percentage error in measuring the radius. Enter your answer as a fraction. ll % (c) One can conclude from the results in (a) and 0)) that O The relative error in the radius must be equal to the relative error in the volume 0 The relative error in the radius must be greater than the relative error in the volume O The relative error in the radius must be less than the relative error in the volume 0 The relative error in the radius does not depend on the relative error in the volume