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Find the differential of the fu cos 2πt 25. z=e-2x

Find the differential of the fu cos 2πt 25. z=e-2x

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter10: Radical Functions And Equations
Section: Chapter Questions
Problem 15CT
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,5) = 6, proximation pproximate ngent plane. it to (5.99) ². me speed v d has been = f(v, t) are able to find on when v mate the or 24 hours 40 9 19 33 -48 67 50 9 19 33 50 69 oximation to near 94°F mate the heat tive humidity SECTION 14.4 Tangent Planes and Linear Approximations 25-30 Find the differential of the function. 25. z e-2x cos 2πt 26. u = 27. m = p³q³ 29. Raß² cos y 28. T = √x² + 3y² V 1 + uvw -y²-z2 30. Lxze = 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. T A 935 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
Transcribed Image Text:,5) = 6, proximation pproximate ngent plane. it to (5.99) ². me speed v d has been = f(v, t) are able to find on when v mate the or 24 hours 40 9 19 33 -48 67 50 9 19 33 50 69 oximation to near 94°F mate the heat tive humidity SECTION 14.4 Tangent Planes and Linear Approximations 25-30 Find the differential of the function. 25. z e-2x cos 2πt 26. u = 27. m = p³q³ 29. Raß² cos y 28. T = √x² + 3y² V 1 + uvw -y²-z2 30. Lxze = 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. T A 935 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
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