Question

1) Sketch the graph?=? ,?=? +3,and include orientation.

2) Sketch the graph ? = sin ? , ? = sin2 ? + 3 and include orientation.

3) Remove the parameter for ? = ? − 3, ? = ?2 + 3? − 2 and write the corresponding

rectangular equation.

4) Remove the parameter for ? = 2 + 3 sin ? , ? = −1 + 3 cos ? and write the corresponding rectangular equation.

5) Create a parameterization for ? = ?2 whose orientation is right to left.

For problem 6-10 use the parametric equations ? = ?2 + 5,? = ?2 − 3? − 1 .

6) Find ??/??

7) Find ?2?/??2

8) Find the slope of the graph when ? = 2

9) Find the intervals on t for which the curve is concave up/down

10) Find the tangent line to the curve at the point (3,6)

For problem 11-14 use the parametric equations ? = ? , ? = 2? − 1 to answer a-e.

11) Find ??/??

12) Find ?2?/??2

13) Find the slope of the graph when ? = ln5

14) Find the intervals on which the curve is concave up/down

15) Find the arc length along the curve defined by ? = 2? − 3 , ? = ?2, on the interval of t values [0,3]. Give an exact answer.

16) Find different polar coordinates for the point (7, 3?/2 ) that satisfy the conditions set forth in

a) ?<0
b) ? < 0

c) any set of coordinates not already used

17) Convert (3, 4?/3 ) from polar to rectangular coordinates.

18) Convert (−7,7√3) from rectangular to polar coordinates.

19) Convert ? = ?2 its corresponding polar equation.

20) Convert ? sin ? = 7 its corresponding rectangular equation.

21) Convert tan ? = 7 its corresponding rectangular equation.

22) Use calculus to find the area of contained by ? = 3 + 3 sin ?

23) Use calculus to find the area inside a single petal of ? = 5 cos 2?

24) Use calculus to find the area inside ?=6sin? outside ?=2+2sin?

25) Use calculus to find the area of the inner figure eight of ? = sin (?/2)

Answer 1