need questions 9, 11, 13, 15, 19, 21, 23, 25 please

C Getting Started 14. r(t) = tanii + sec j + costk 1. What is the derivative of r(t) = ((.).&(t)h(t))? 15. r(t) = (test Int. cost) 2. Explain the geometric meaning of r' (t). 16. r) = (+ 1),tan. In ( + 1)) 3. Given a tangent vector on an oriented curve, how do you find the 17-22. Tangent vectors Find a tangent vector at the given value of unit tangent vector? for the following parameterised curves. 4. Computer") when r(t) = (10.81, cost). 17. r(t) = (1, 30.2").1 = 1 18. r(t) = (2,4",).1 = 0 5. How do you find the indefinite integral of r(t) = ((.).(t). (1) X? 19. (1) (t. ces 2t, 2 sint),1 = 6. How do you evaluate (1) 2 7. Find Cifr()-(3 cos II + 10) + C and r(0) = (0,0,0). 20. (1) - , 3 8. Find the unit tangent vector at 1 = 0 for the parameterized curve 10 r(t) ifr' (1) = (+ 5. sint + 2. cos! + 2). 21. r(t) - 2r'i + 6+ k! Practice Exercises 22. r(t) = xi + *} + 4ck, 1 = In 3 9-16. Derivatives of vector-valued functions Differentiate the follow ing functions 23-28. Unit tangent vectors Find the unit tangent vector for the following parameterized curves 9. r(t) = (cos!,,sin) 10. r(t) = 4d'I + 5j + Ink 23. r(t) = (21.21.I), for OSISI 12. r(t) = (4.3 cos 21. 2 sin 3r) 24. r(t) = (cost, sin t. 2). for 0 SI 27 13. r(t) = di + 2e 'j - 4ek 25. r(t) = (8.cos 21, 2 sin 21), for OSIS 2 = (2 sin 1, 3 cos t, sina)=- : 11. (o) - (27.v.)