Name SID Section
1
practice midterm 2
math 21a
feb 20, 2004
1. What is the equation of the line tangent to y = cos(x) at the point ( , 1 )?
3 2
2. Consider the parabola dened by the equation p(x) = (x + 1)2 + 4. Where do the lines
tangent to p(x) at x = 0

MAT21B (Kppe): Midterm I
o
Please ll out the following.
Name:
Student Id:
We ll out the following when we grade this exam.
Problem
1
2
3
4
5
6
7
8
5
5
5
5
5
5
5
5
Points
of
Total:
Please write your answers in the provided space, and show your work.
A shee

Math 21B-B (Koeppe):
Midterm II
Please ll out the following.
Name:
Student Id:
We ll out the following when we grade this exam.
Problem
1
2
3
4
5
6
7
8
Points
of
20 20 20 20 20 20 20 20
Please write your answers in the provided space, and show your work.

Name SID Section
1
practice midterm 2 solutions
math 21a
feb 20, 2004
1. What is the equation of the line tangent to y = cos(x) at the point ( , 1 )?
3 2
y
1
2
=
3
2 (x
)
3
2. Consider the parabola dened by the equation p(x) = (x + 1)2 + 4. Where do the

Fall 2005
MAT 21D-1: Practice Midterm II
Instructor: Kei Nakamura
1. Let f (x, y, z) = ln(x2 + y 2 ).
(a) Find the gradient of f .
(b) Determine whether or not f is harmonic.
2. Let F = x2 y, exyz , sin(xz 2 ) .
(a) Find the divergence of F.
(b) Find the