Calculus Problems

1. Graph the curve C defined by the parametric equations: X x=t-1 t y = t+ 1 2. Determine if C has any horizontal or vertical tangent lines. 5 3. Find the area bounded by C and the 4. Does the curve C intersect or collide with any points on the curve S = { (t² - 1, t+ 1)|t e R}. 5. Find all points where the curve defined by r = 1 + 2cos0 has horizontal & vertical tangent lines. Graph this curve. 6. Find the area enclosed by the inner loop of the curve defined by r = 1 + 2cos0. 7. Determine the equation of the tangent line(s) to the curve defined by r = 1 + 2cos0 where the curve intersects the curve defined by r = 1 + cose Write these lines in rectangular form. 8. Find the length of the curve r =1 + cosê. (Yes, I do mean the length). 9. Find the surface area of the curve r = 1 + coso rotated around x-axis. 10. Find the surface area of the curve r = 1 + cose rotated around y-axis.