31,37 proximation of the functioncos y at (1, 1) and use it to approximatetrate by graphing f and the tangent plane.roximation of the functiony2 + z² at (3, 2, 6) and use it tomber √(3.02)2 + (1.97)² + (5.99) ².in the open sea depend on the speed vlength of time t that the wind has been. Values of the function h = f(v, t) arehe following table. Use the table to findon to the wave height function when vis near 20 hours. Then estimate theme wind has been blowing for 24 hoursDuration (hours)1520816253647817284054Deed (km/h)309501831456260409-35 -3619-41 -42 -43334867e 3 to find a linear approximation towhen the temperature is near 94°Fis near 80%. Then estimate the heature is 95°F and the relative humidityis the perceived temperature whenT and the wind speed is v, so we canollowing table of values is an excerpt4.1. Use the table to find a lineard-chill index function when T is50 km/h. Then estimate the wind-erature is -17°C and the wind-21 -22 -23 -23-27 -29 -30 -30-347050-379-441933506927. mp³q³29. Raß2 cos yV1 + uvw30. L=xze-²-²31. If z = 5x² + y² and (x, y) changes from (1, 2) to (1.05, 2.1),compare the values of Az and dz.28. T=32. If z = x² - xy + 3y2 and (x, y) changes from (3,-1) to(2.96,-0.95), compare the values of Az and dz.33. The length and width of a rectangle are measured as 30 cmand 24 cm, respectively, with an error in measurement of atmost 0.1 cm in each. Use differentials to estimate the maxi-mum error in the calculated area of the rectangle.xl of FP34. Use differentials to estimate the amount of metal in a closedcylindrical can that is 10 cm high and 4 cm in diameter if themetal in the top and bottom is 0.1 cm thick and the metal inthe sides is 0.05 cm thick.35. Use differentials to estimate the amount of tin in a closed tincan with diameter 8 cm and height 12 cm if the tin is 0.04 cmthick.loqqu236. The wind-chill index is modeled by the functionW = 13.12 +0.6215T 11.370.16 + 0.3965Tv0.16T =where T is the temperature (in °C) and v is the wind speed(in km/h). The wind speed is measured as 26 km/h, with apossible error of ±2 km/h, and the temperature is measuredas -11°C, with a possible error of ±1°C. Use differentials toestimate the maximum error in the calculated value of W dueto the measurement errors in T and v.37. The tension T in the string of the yo-yo in the figure ismgR2r² + R²Rwhere m is the mass of the yo-yo and g is acceleration due togravity. Use differentials to estimate the change in the tensionif R is increased from 3 cm to 3.1 cm and r is increased from0.7 cm to 0.8 cm. Does the tension increase or decrease?38. The pressure, volume, and temperature of a mole of an idealgas are related by the equation PV = 8.317, where P is mea-sured in kilopascals, V in liters, and T in kelvins. Use differ-entials to find the approximate change in the pressure if thevolume increases from 12 L to 12.3 L and the temperaturedecreases from 310 K to 305 K.

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ate ane. 2 n те d 5 S 5 at y n ot 1+ uvw 30. L=xze-²-² 29. Raß² cos y 31. If z = 5x² + y² and (x, y) changes from (1, 2) to (1.05, 2.1), compare the values of Az and dz. 32. If z = x² - xy + 3y2 and (x, y) changes from (3,-1) to (2.96,-0.95), compare the values of Az and dz. 33. The length and width of a rectangle are measured as 30 cm and 24 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maxi- mum error in the calculated area of the rectangle. 34. Use differentials to estimate the amount of metal in a closed cylindrical can that is 10 cm high and 4 cm in diameter if the metal in the top and bottom is 0.1 cm thick and the metal in the sides is 0.05 cm thick. 35. Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height 12 cm if the tin is 0.04 cm thick. 36. The wind-chill index is modeled by the function W = 13.12 + 0.6215T-11.370.16 + 0.3965Tv0.16 where T is the temperature (in °C) and v is the wind speed (in km/h). The wind speed is measured as 26 km/h, with a possible error of ±2 km/h, and the temperature is measured as -11°C, with a possible error of ±1°C. Use differentials to estimate the maximum error in the calculated value of W due to the measurement errors in T and v. 37. The tension T in the string of the yo-yo in the figure is mgR 2r² + R² T= where m is the mass of the yo-yo and g is acceleration due to gravity. Use differentials to estimate the change in the tension if R is increased from 3 cm to 3.1 cm and r is increased from 0.7 cm to 0.8 cm. Does the tension increase or decrease? H 38. The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV = 8.31T, where P is mea- sured in kilopascals, V in liters, and T in kelvins. Use differ-

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...