Math 016A Name: ID
Final Signature
Mar., 2009
Show all your work to get full credits! No Calculators allowed. 1. Evaluate the following limits and derivatives: (a)[16pts]
x2
lim
x2 3x + 4 x2
2
3x2 x x + 2 lim
(b)[16pts] d dx x2 x+1
d 2x 16 x2 dx
1
2. (2
Math 016A Name: ID
Midterm 2 Signature
Mar., 2009
Simplify your nal result if possible. No Calculators allowed. 1. (20pts)[a](8pt) Find the derivative of f (x) = [x2 (2x + 3)]3 .
[b](12pt) Find the second derivative and solve the equation f (x) = 0 for f
Math 016A Name: ID
Midterm 1 Signature
Jan., 2009
No Calculators allowed. Use the back of all the pages if needed. 1. (20pts)(a)[8pts] Given the endpoints of a diameter for a circle: (3, 3), (3, 3), nd the general form of the equation of the circle.
(b)[1