MTH130 Module 2 - Section Assignment 3.7 (Homework)

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Estimating the Amount of Rust-Proofer Required A hemisphereishaped dome of radius 70 ft is to be coated with a layer of i'ustiprooi'er before painting. Use differentials to estimate the amount of rustiproofer needed if the coat is to be 0.01 in. thick. [Round your answer to two deCImal places.) Hint: The volume of a hemisphere of radius r is V = .'rr3. 3 Effect of Capital Expenditures on GDP An economist has determined that a certain country's gross domestic product {GDP} is approximated by the following function where f(x) is measured in billions of dollars and x is the capital outlay.r in billions of dollars. x) : 53 tux\" Use differentials to estimate the Change in the country's GDP if the country's capital expenditure changes from 5253 billion to $258 billion. (Round your answer to two decimal places.) $ |:| billion dollars Let y = ((x), where R(x) = 4x- + 4. Find the differential of the function. dy =Let fbe the function defined as follows. y=f[x)=3x23x+7 (a) Find the differential of f. {b} Use your result from part (a) to nd the approximate change in y ifx changes from 2 to 13?. [Round your answer to two decimal places.) (c) Find the actual change in y ifx changes from 2 to 1.9? and compare your result with that obtained in part (b). (Round your answer to two decimal places.) Let f be the function defined as follows. y = f(x) = \\ 7x + 2 (a) Find the differential of f. dy = (b) Use your result from part (a) to find the approximate change in y if x changes from 4 to 4.1. (Round your answer to three decimal places.) dy = (c) Find the actual change in y if x changes from 4 to 4.1 and compare your result with that obtained in part (b). (Round your answer to three decimal places.) Ay =Use differentials to approximate the quantity. (Give your answer correct to 4 decimal places.) V 65Use a differential to approximate. (Give your answer correct to 4 decimal places. ) 6(1.98) (1.98)2 + 1Estimating the Amount of Paint Required A coat of paint of thickness 002 cm is to be applied uniformly to the faces of a cube of edge 27 cm. Use differentials to find the approximate amount of paint (in cm3} required for the job, correct to the nearest cubic centimeter. Hint: The volume of a cube of edge 5 is V = 53