caps lock shift Exercises In Exercises 1-6, calculate r'(t) and T(t), and evaluate T(1). In Exercise 1. r(t) = (412, 91) 2. r(1) = (e', 12) 20. (12 , 13 3. r(1) = (3+41,3-51, 91) 4. r(1) = (1+ 21,12, 3-12) 31. (t cos 5. r(t) = (cos at, sin it, t) 6. r(1) = (e', e-, 12) 33. Let In Exercises 7-10, use Eq. (3) to calculate the curvature function k(t). that the r 7. r(t) = (1, et , 1) the Bern 8. r(t) = (4 cost, t, 4 sint) 34. The 9. r(t) = (41 + 1, 41 - 3, 21) 10. r(1) = (t-1, 1, 1) Osts In Exercises 11-14, use Eq. (3) to evaluate the curvature at the given point. (a) Sho (b) Wl 11. r(t) = (1/t, 1/12, 12), t = -1 (c) Fo 12. r(t) = (3 - t, et-4, 81 - 12), 1 = 4 cloid those 13. r(t) = (cost, sint, 12), 1 = 14. r(t) = (cosh t, sinh t, t), t = 0 (x 301) Doing In Exercises 15-18, find the curvature of the plane curve at the point indicated. 15. y = et, t =3 16. y = cos x, x = 0 17. y = 14, 1 = 2 18. y = th, t = 1 19. Find the curvature of r(t) = (2 sint, cos 3t, t) at t = 3 and t = ?. 20. CAS Find the curvature function k(x) for y = sin x. Use a com- puter algebra system to plot k(x) for 0