Lecture 5
Topics to Cover
3.5:
methods of nding limits (Ex. 3D: all)
sin
=1
0
lim
3.6:
innite limits (Ex. 3E: all)
3.7:
limits at innity
Shortcut Method for some Problems Involving
Trigonometric Functions
Does NOT work if angle is not
means that
sin (an
AMA1100
() =
Week 7
Tutorial Problems
2, 3
2, > 3
1) Find the left hand limit and right hand limit at 3 for f. Is it continuous at this point?
() =
3 2, 2
2, > 2
2) Find the left hand limit and right hand limit at 2 for f. Is it continuous at this point
Lecture 6
Topics to Cover
4.1:
tangents to a curve, slope of a curve at a point
DERIVATIVE of a function
f () f (x)
x
f (x + x) f (x)
f (x + h) f (x)
= lim
= lim
xx
x0
h0
x
h
xx
f (x) = lim
4.1.4:
dierentiability = continuity
4.1.5:
rate of change, speed
THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Applied Mathematics
AMA1100
Week 04
1. Suppose 0 x, y . If sin x =
2
(a) sin (x + y)
1
3
and sec y = 5 , evaluate the following expressions.
4
(b) cos (x y)
(c) sin 2y
2. (a) Find all possible values of s
THE HONG KONG POLYTECHNIC UNIVERSITY
Department of Applied Mathematics
AMA1100
Week 03
1. Solve the following inequality.
2x 3
0
5
(b) 2 (3x 2) 4 x
2x 5
2x + 1
< 2 and
>0
2
3
(d) 1 x < 7 + x or 4x + 3 > x
(a)
(c)
2. Solve the following absolute value ineq
How to Study Maths?
You are now a university student. The correct way to study mathematics is very
different from how it was in middle school.
The teacher will no longer teach you everything you need to know; nor will he give
you every possible example an
AMA 1100 Class Problems
Lecture 5
Full Name (in English): Student No.:
1 _ sin(rc) +9;
1' ta.11(7$)
Use your calculator to calculate f for :1: = 0.1, 0.0001, 0.0000001 and :1: = 70.01,
0.00001. Can you guess what is limnHO f
Using calculators to nd li
Problems on Inverse Functions Asked by a Student
For each of the function f (x), (i) choose a suitable domain so that an inverse exists, and (ii)
nd the inverse function f 1 (x)
(a)
1
x6
First of all, x cannot be 6 because that will make the denominator 0
AMA 1100
Class Problems Answers
Lecture 1
1. Solve the inequality
Sorry, it is typing
mistake. Should be >
|3x + 1| > 7.
3x + 1 < 7 or 3x + 1 < 7
3x < 8 or 3x < 6
8
x<
or x < 2
3
2. Plot the graph of
y = 2x2 |5x| x with the domain [3, 4].
Some people try
Lecture 3
Topics to Cover
2.6:
exponential functions; law of indices (whole of Ex. 2G)
2.7:
logarithmic functions; rules of log
See a simulated slide rule by clicking here
* In the study of radioactive decay.
Lecture 1
Topics to Cover (See also Foundation Mathematics Basic Concepts)
1.2:
Simple inequalities
(Ex. 1B: 111)
1.3:
absolute value, |x|
1.4:
function; input, argument, independent variable; output, dependent variable
1.5:
how to draw graphs of function
Limits
3.1:
One-sided Limits (Ex. 3A: all)
3.2:
Limits of Functions (Ex. 3B: 1-5)
3.3:
Limit Theorems (Ex. 3B: 1-5)
Why Limits? Sometimes a function dened by a formula, e.g.
f (x) =
x + x2
sin(x)
works OK MOST of the times, but the formula fails for
x = 0