hello can I please have some help here , can you please write on a sheet of paper and not on your keyboard please ?

Section 11.4: 17. 18 (no sketch, find tangent lines)

Section 11.5: 1 - 6

EXERCISES 11.4 Symmetries and Polar Graphs Graph the lemniscates in Exercises 13-16. What symmetries do these Identify the symmetries of the curves in Exercises 1-12. Then sketch curves have? the curves in the xy-plane. 13. r2 = 4 cos 20 14. r2 = 4 sin 20 1. r = 1 + cos 0 2. r = 2 - 2 cos 0 15. r2 = -sin 20 16. r2 = -cos 20 3. r = 1 - sin 0 4. r = 1 + sin 0 Slopes of Polar Curves in the xy-Plane Find the slopes of the curves in Exercises 17-20 at the given points. 5. r = 2 + sin 0 6. r = 1 + 2 sin 0 Sketch the curves along with their tangents at these points. 7. r = sin (0/2) 8. r = cos (0/2) 17. Cardioid r = -1 + cos 0; 0 = +1/2 18. Cardioid r = -1 + sin 0; 0 = 0, T 9. r2 = cos 0 10. r2 = sin 0 19. Four-leaved rose r = sin 20; 0 = + 1/4, +31/4 11. r2 = -sin 0 12. r2 = -cos 0 20. Four-leaved rose r = cos 20; 0 = 0, + 1 /2, TTFinding Polar Areas Find the areas of the regions in Exercises 18. 1. Bounded by the spiral r = B for 0 E B 5 7r r= 23inl9 3. Inside the oval limacon r = 4 + 2 cos 6 4. Inside the cardioid r = 0(1 + cos 6), a > O 5. Inside one leaf of the four-leaved rose r = cos 26 6. Inside one leaf of the three-leaved rose r = cos 36 y r = cos 38