Spans are subspaces
Don't do row operations on matrices when finding eigenvalues
Try to avoid anything but row additions when trying to find determinant
unless u will be extra careful
Ortho of column space is null space or tho of row space is transpose of
How to solve inconsistent systems
Matrix equation has solution if b is in column space of A
What is a unique solution?
Rank is full if there is a unique solution
If rank isn't full, nullity can be 1 or more, infinite solutions, free variable
MATH 152 Dr. Z. , Practice For Make-Up Exam I: Pracice A1,
1. (10 points [5 each]) Find the following indefinite integrals
x cos 3x dx
3(x + 2)
+ 4x + 4)(x + 1)
2. (10 points ) The base of a solid is the region inside
Commutative Property of Addition
Associative Property of Addition
Commutative Property of Multiplication
Associative Property of Multiplication
0 < w < 12
0 < w > 12
12 < w < 0
12 > w < 0
None of these
How is the graph in part b related to the graph in part a? If a graph is not supposed to be stretched or
shrunk, enter 1 in the corresponding box on the right. If a graph is not supposed to be shifted in some
direction, enter 0 in the correspo
1. (J6po'mts) Let A =
4 3 1 1 1 _ _
,B[_1 O 1],C[2 _1],andvl:21].
Find the following or say it doesnt exist:
(a)BA2CT 1+ 3 1! 1 ll
[,1 01 21 2 [ 2, (10 points) For the following, write true or false. No justication is needed.
(a) A set
Linear Algebra, Math 250
Section C2, Fall 2016
Midterm Exam 2
November 16, 2016
NAME: 5 O I urllbS
Attempt all problems, and show all of your work.
You may NOT use textbooks or calculators on this exam.
l Problem Number Possible Points Points Earned
g eN g 1
g ~ g g e
7.1-7.5 Practice Problems
cos(5x) + e2x + tan(2x)dx
ex +2 dx
x2 (ln(x)2 dx
x2 ex dx
sin4 x cos3 xdx
Math. 152, Problems for the streaming review for exam 2.
Sara Nadiv Soffer
1. (a) Find the 4th Maclaurin polynomial of the function f (x) = e2x .
(b) Use (a) to approximate e0.2
(c) Find the remainder of the approximation in (b).
2. Find the limit of the