MATH237: EXAM-AID SOS
NIALL W. MACGILLIVRAY (EDITOR); VINCENT CHAN (WRITER)
October 30th, 2010
1.
Scalar Functions (1.1-1.2)
DEFINITION 1.1. Suppose A and B are sets. A function f is a rule that determines
how a subset of A is associated with a subset of
MATH 237 MIDTERM
Ryan Ali
Outline
1.1-1.2 Scalar Functions
2.1-2.2 Limit Theorems
2.3-2.4 Proving a Limit Does (Not) Exist
3.1-3.2 Continuity Theorems
3.3
Limits Revisited
4.1-4.2 Partial Derivatives
4.3-4.4 Linear Approximations
5.1
Differentiability
Out
1- Let ($,y,z) = T(r,0,z) = (r c030, 1" sin 0, z).
5(m, y, 2)
0(7‘, 0, z) '
2- Chapter 13 page 163 # 5(a).
Find the J acobian
3- Let (u,v) = F(x, y) = (e35 cos(7ry), ex sin(7ry) .
Let St, = my) : m s 0.1, lyl s 0.1} and Try = {(m) = m :1, Iyl £1}.
(a) F