Please only help with questions 1, 3,7,11, 13, 17, 21. Thank you!

3.10 EXERCISES 15-18 (a) Find the differential dy and (b) evaluate dy for the 1-4 Find the linearization L(x) of the function at a. given values of x and dx. 1. f ( x) = x3 - x2+ 3, a=-2 15. y = etho, x = 0, dx = 0.1 2. f(x) = sin x, a = 1/6 16. y = Cos TX, x = 3, dx = -0.02 3. f ( x ) = Vx, a = 4 17. y = \\3+x2, x =1, dx = -0.1 4. f ( x) = 21 , a = 0 18. y =- x+ 1 x = 2, dx = 0.05 x - 5. Find the linear approximation of the function f(x) = 1 - x at a = 0 and use it to approximate the numbers v0.9 and v0.99. Illustrate by graphing f and the 19-22 Compute Ay and dy for the given values of x and tangent line. dx = Ax. Then sketch a diagram like Figure 5 showing the line 6. Find the linear approximation of the function segments with lengths dx, dy, and Ay. g(x) = VI + x at a = 0 and use it to approximate the 19. y = x2 - 4x, x = 3, Ax = 0.5 numbers 10.95 and 1.1 . Illustrate by graphing g and the tangent line. 20. y = x - x', x = 0, Ax = - 0.3 A 7-10 Verify the given linear approximation at a = 0. Then 21 . y = Vx - 2, x =3, Ax =0.8 determine the values of x for which the linear approximation is 22. y = ex, x = 0, Ax = 0.5 accurate to within 0. 1. 7. In(1 + x) ~ x 8. (1 + x) 3~ 1 - 3x 23-28 Use a linear approximation (or differentials) to estimate 9. V 1 + 2 x ~ 1 + 2x 10. ecos x ~ 1 + x the given number. 23. (1.999)4 24. 1/4.002 11-14 Find the differential of each function. 25. 1001 26. 100.5 11. (a) y = xe -4x ( b) y = v1 - +4 27. 20.1 28. cos 290 1 + 2u 12. (a) y = 1 + 3u (b) y = 02 sin 20 29-31 Explain, in terms of linear approximations or differen- 13. (a) y = tan Vt 1 - v2 ( b) y = tials, why the approximation is reasonable. 1 + 0 2 29. sec 0.08 ~ 1 30. 4.02 ~ 2.005 14. (a) y = In(sin 0) ( b ) y = ex 1 - et 31. 9.98 ~ 0.1002