ECON1001/7001
Tutorial Problems / Questions - Week 05
Problem 1
Compute the derivatives of the functions with the formulas below:
Problem 2
For each total cost fuction, ﬁnd the marginal cost, denoted C’ (q), the
average total cost, denoted ATC (q), th

ECON1001/7001
Tutorial Problems/ Questions - Week 06 (2016)
Problem 1
Compute the ﬁrst and second derivatives of the functions f : (0, +00) —>
R below.
(1a) f(:r) 3x9 — Sac—0‘5
(1b) f(x) 77r — 1
(10) f(x) = g(a:)h(x), where g : (0,+00) —> R and h : (0,+00

ECON1001/7001
Tutorial Problems / Questions - Week 03
Problem 1
Read Newton’s Binomial Formula and Pascal’s Triangle in chapter 3.
(1a) Expand (2my2z‘1 — 3x3y‘122)6.
(1b) Find the coefﬁcient of $25 in the expansion of (2x2y3 + x/y)”.
Problem 2
Find the su

ECON1001/7001
Tutorial Problems / Questions - Week 02
The solutions will be presented during tutorial sections.
Discussion about Bonus Problems will only occur if time per-
mits.
Problem 1
(1a) Write the mathematical formula of any function that has a gra

EMET1001/7001
Week 4 Lecture 1
Affine Functions
have graphs that are straight lines
f: R R such that for every x R:
f(x) = mx + b, with b, m R
Increasing Affine Functions
y
8
6
4
2
-4
-3
-2
-1
1
-2
-4
-6
2
3
4
5
6
7
x
Decreasing Affine Functions
y
12
10
8

EMET1001/7001
Week 3 Lecture 2
Sigma Notation
A Bit of Logic
Symbol for implies that
Symbol for equivalent to
Examples: A B reads A implies B, or
B is a necessary condition for A, or A
is a sufficient condition for B, B occurs
if A occurs, A occurs onl

EMET1001/7001
Week 2 Lecture 1
2
Integer Numbers Z
Integer numbers: positive, zero and negative
numbers, Z = cfw_ , 3, 2, 1, 0, 1, 2, 3,
Multiplication: integer numbers are closed with
respect to multiplication
Division a/b: we find q and r such that:

EMET1001/7001
Week 3 Lecture 1
Affine Functions
have graphs that are straight lines
f: R R such that for every x R:
f(x) = mx + b, with b, m R
Affine Functions
For every x R:
f(x) = mx + b, with constants b, m R
This function is constant if and only if m

EMET1001/7001
Week 5 Lecture 1
About Functions
Typically, graphs of functions are
not straight lines
Well-behaved functions have
graphs that are close to straight
lines locally, as we zoom in
y
0.9
f(x) = x2
and the
tangent
line at
the point
(0.5, 0.25)
0

EMET1001/7001
Week 4 Lecture 2
Limits of Functions
The limit of function f, as x tends to a,
denoted x a, is equal to L if f(x) is close to
L when x is close to a. The notation x a
reads x converges to a, x goes to a, or x
tends to a, or x approaches a) m

EMET1001/7001
Week 1 Lecture 1
2
What is this course about?
This course is an introduction to Calculus and
Optimization from the viewpoint of Economics
and Finance.
We plan to have lots of FUN ( first priority )
and, in the process, to learn some interest