AMA 1104
Assignment 1
1st Sem, 2014 - 2015
Due date: October 10, 2014, 5:20 pm. No late submission accepted.
To be handed in to me directly or in my mailbox at HJ 611.
1. (20 points) In a high school class of 100 students, 55 studied history, 60 studied m

Todays topics
(1) First principle; existence of derivatives/differentiable
Lec 6Chapter 3
Yijun Lou
(2) Techniques of differentiation
Oct 17, 2016
2/27
First principle:
I
4x
if x 6 0 ;
If f is
ax + b if x > 0 .
differentiable at x = 0, find the values of

Todays topics
(1) More examples on limits
Lec 5Chapter 3
Yijun Lou
October 3, 2016
(2) Continuous functions; Intermediate value theorem
(3) First principle
2/27
Additional Example 7:
Methods of evaluating limits
(a)
(1) Substitution (always try this metho

Todays topics
(1) Why study Probability and Statistics?
Lec 8Chapter 10
Yijun Lou
Oct 31, 2016
(2) Counting Rules
(3) Venn Diagram
(4) Basic probability rules: Addtion rule, Complement
(5) Marginal Probability
2/38
Experiments and Sample Space
Chapter 10.

AMA1110: Supplement Exercises 7
1. Suppose f ( x ) is a function and f 0 ( a) exists. evaluate the following limits:
(a) lim
x 0
f ( a) f ( ax )
x
(b) lim
f ( a+4h) f ( a)
h
(c) lim
f ( a+4h) f ( ah)
h
h 0
h 0
d
1
cos1 x =
for | x | < 1 by using the form

AMA1110: Supplement Exercises 6
1. Prove that
d(sin x )
dx
= cos x.
2. Evaluate the derivative of y =
x3
cos x :
(1) by using the quotient rule as y =
f (x)
g( x )
with f ( x ) = x3
and g( x ) = cos x; (2) by employing the product rule as y = f ( x ) g( x

AMA1110: Supplement Exercises 5
1. For the function
9 x2
,
3( x + 3)
f (x) =
sin 2x tan x
,
2x2
0,
3 < x < 0;
0 < x < 1;
x = 0.
(a) Find the following (one-sided) limits if they exist (or explain if it does not exist)
(i) lim f ( x )
x 3+
(ii) lim f ( x )