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- Determine dimension x to 3 decimal places.A coat of paint of thickness 0.02 cm is to be applied uniformly to the faces of a cube of edge 21 cm. Use differentials to find the approximate amount of paint required for the job, correct to the nearest cubic centimeter.Suppose a metal rod has length 20 cm and diameter 6 cm. If it is to be insulated, except for the ends, with a material 0.001 cm thick, determine the estimated volume of the insulation using differentials.
- evaluate the definity integral from -10 to 10 (2 - x)dxThe marginal cost function for the manufacture of headphones is given by: where x is the number of headphones manufactured. Use a Riemann sum with n = 5 toestimate the cost of producing the first 5 headphones.3) Use differentials to estimate the relative error in the lateral surface area of a right circular cylinder if the diameter is measured to be 10 in. with a possible error of 0.01 in. and the height is equal to its diameter.
- Assume that a company's marginal cost function for the manufacture of x phones per hour is c(x) = 180 − 0.006x, and that they sell the phone for an average wholesale price of $520. Use a Riemann sum with n = 5 subdivisions to estimate the total additional hourly profit corresponding to an increase in production and sales from 10,000 to 20,000 phones per hour. (Use a left Riemann sum to find your answer.)A company manufactures mountain bikes. The research department produced the marginal cost function C′(x)=700−x3, 0≤x≤900, where C′(x) is in dollars and x is the number of bikes produced per month. Compute the increase in cost going from a production level of 300 bikes per month to 720 bikes per month. Set up a definite integral and evaluate it.Other than using definite integrals, how else can you solve areas of regions bounded by curves