19,25,31 19. Given that f is a differentiable function with f(2,5) = 6,fr(2, 5) = 1, and fy (2, 5) = -1, use a linear approximationto estimatef(2.2, 4.9).20. Find the linear approximation of the functionActual temperature (°C)f(x, y) = 1- xy cos y at (1, 1) and use it to approximatef(1.02, 0.97). Illustrate by graphing f and the tangent plane.21. Find the linear approximation of the functionf(x, y, z) = √√x² + y² + z² at (3, 2, 6) and use it toapproximate the number √(3.02)2 + (1.97)2 + (5.99) ².22. The wave heights h in the open sea depend on the speed vof the wind and the length of time t that the wind has beenblowing at that speed. Values of the function h = f(v, t) arerecorded in feet in the following table. Use the table to finda linear approximation to the wave height function when vis near 40 knots and t is near 20 hours. Then estimate thewave heights when the wind has been blowing for 24 hoursat 43 knots.Wind speed (knots)402030-15-20t50 19T- 10-25560 24V145920- 18- 24<-30-37101321788293730Duration (hours)- 2015- 26-3316- 39253647Wind speed (km/h)4020- 21-2732017- 342823. Use the table in Example 3 to find a linear approximation tothe heat index function when the temperature is near 94°Fand the relative humidity is near 80%. Then estimate the heatindex when the temperature is 95°F and the relative humidityis 78%.01 SUBUIS-414024. The wind-chill index W is the perceived temperature whenthe actual temperature is T and the wind speed is v, so we canwrite W = f(T, v). The following table of values is an excerptfrom Table 1 in Section 14.1. Use the table to find a linearapproximation to the wind-chill index function when Tisnear -15°C and v is near 50 km/h. Then estimate the wind-chill index when the temperature is -17°C and the windspeed is 55 km/h.5450- 22- 2930- 359- 421831456260- 23-3040-369- 431933486770- 23- 3050-379- 4419335069SECTION 14.4 Tangent Planes and Linear Approximations25-30 Find the differential of the function.25. ze 2x cos 2πt27. m = p³q³29. R = aß² cos y-26. u = √√x² + 3y²V28. T31. 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 = x²xy + 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.O=T=1 + uvw30. L = xze-²-2²11Phot 12.034. 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.93535. 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.36. The wind-chill index is modeled by the functionW = 13.12 + 0.6215T - 11.370.16 +0.3965Tv0.16where 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 isHow 10KR++mgR2r² + R²Uwhere 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?ΤΑ38. 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.

note :- since you have asked multiple questions but according to bartleby guidelines i only have to…

Answered: 19. Given that f is a differentiable…

19. Given that f is a differentiable function with f(2, 5) = 6, fr(2,5) = 1, and fy (2, 5) = -1, use a linear approximation to estimate f(2.2, 4.9).

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...