Reference no: EM13910588

1. Find dy/dx and d²y/dx². For which values of t is the curve concave upward?

x=t³ + 1, y = t² - t  

2. Find the points on the curve where the tangent is horizontal or vertical.

x = t³ - 3t,  y = t³ - 3t²

3. Find the equation of the tangents to the curve

 x = 3t² + 1,  y = 2t³ + 1  , that pass through the  point (4, 3).

4. Find the area enclosed by the x-axis and the curve

x = 1 + e^t,  y = t - t².

5. Find the length of the loop of the curve

x = 3t - t³,   y = 3t².

6. Sketch the curve and find the area that it encloses.

 r = 4 + 3sinθ

7. Find the area of the region that lies the curve r = 2 + sinθ and outside the curve r = 3sinθ.

8. Find the area of the region that lies inside both curves.

r = 1 + cosθ,  r = 1 - cosθ

9. Find the exact length of the polar curve.

r = 2(1 + cosθ)