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  3. Stellenbosch University (SUN)
  4.  
  5. Mathematics 144 (MATH114)

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Summary Mathematics 114 summaries
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  • Course
  • Mathematics 144 (MATH114)
  • Institution
  • Stellenbosch University (SUN)
  • Book
  • Single Variable Calculus

Aesthetic digital concise summaries of all the theory and some examples you need to know for mathematics 114. The whole semester's content for mathematics 114 is summarised. Self-study: Revision of coordinate geometry & straight lines These are topics that you should be familiar with from school...

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  • No
  • All chapters covered in mathematics 114
  • June 1, 2022
  • 80
  • 2021/2022
  • Summary

Subjects

  • math
  • mathematics 114
  • mathematics 114 summaries
  • maths 114
  • maths 114 summaries
  • mathematics summaries
  • calculus semester 1
  • calculus 114
  • mathematics calculus
  • calculus summaries
  • 114

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  • Stellenbosch University (SUN)
  • Mathematics 144 (MATH114)
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Content preview

Numbers
•

IR : real numbers

•
IN :
integers ( -2 , 1,0 )

④ rational numbers of
: → ratio
integers
•




→
decimal representation is always repeating
0,50
'
e-
g z
=




É =

0,6666 =
0,5
•
Irrational numbers > cannot be expressed as ratio of integers 11T
,
B
,
1091027
•

IN : natural numbers : [ 1. 2,3 . . . }




°:"^°ᵗ°^"Mb"[)
•
W : whole : 0
, 1,2 3,4 , . . -




± "" " "

if acb then btc (
•
ate <
symbol representing
◦
a
very large number
positive
$




u w Proof by contradiction (§ < 1)
it is between a and b
x exists if
o
{ xlacxcb }
o


Open : Ca , b) =



y g
⑧

{
⑧

Closed : [a ,b] = xla≤ ✗ ≤ b}
, t
a b




solving inequalities : 4x < 2×+1 ≤ 3×+2 / split
,
1




Absolute values

191 ≥ 0 for number a.
every

191=9 if a ≥ 0


191 = -

a if 9<0




az = 1011 for all values of a
,
as a must be ≥ 0 .

, properties
lab / lallbl 13×-21
e. g.
just
=
•
*


b≠0 191
§
•
= 191 =

i




{
/ by
= 1011 = a if a ≥o
a if a < 0
Ian / 1AM NEZ
-


• =

,


•
1×1 =
9 if I = -1-9

•
txt < a if -
a < ✗ < a


•

1×1 > g if ✗ c- a or x > a




e.
g. with
inequalities :




0<1×-51 < É } split

9




{
<
a txt 1×1
0<1×-51 1×-51 < É

X -
5 > 0 or
-



t < x -
S <
{

x -

5 < 0
{ < ✗ <
¥
0 °
i. ✗ < 5 Or × > 5 >
◦
<
I ,

4 'z 5 5
;
i. ✗ E ( 45 5) ,
U / 5. ¥ )

triangle inequality
latbl ≤ 101 -1lb /




and radians
trigonometry
180
✗

radian *
> degree
^




9,0° /
0° 30° 45° 60° 180° 360°
Cosa
Degrees
¥
=




IT IT IT ± 10,1) PE
0 IT 21T
Radians 3- and r=t
6- -4 ( cosy sino )
p⊖ ,
( x , y) : ✗ = ( 050
length of arc


( 1 radian = where a = r
A
a = TO I -1,07
5 OF Poll ,O )
< >
Pit
C
T
Sino =

?
tano =
y
1)
Pgp
co , -




, I
I ≤ 1 I I
[ Oso ≤ and ≤ Sino
-


≤ v
-




COSO =
¥

,Trigonometric identities


•
( 0sec / ⊖ ) = I

Sino I I
'
4 3
• Sec ⊖ = I
z z
COS ⊖ I
,
I
•
cot ⊖ = = COS -0
tano Sino
IT
I
¥
sin ⊖ I
• tan -0 = 3

( 050



PYTHAGOREAN IDENTITIES CO -
FUNCTIONS


(0520--1 Simo 1 (¥ ⊖)
=

cos
-
=
Sino
÷ sink
sin (
÷ cosy
Iz ⊖ )
OSOS
-
= [


L



Sec 20 = I + tan 20 [ 0sec 20
=
1+101-20


EVEN AND ODD DOUBLE ANGLES



[OSC -
⊖) = COSQ sin C- F) =
-
Sino
sin 20 =
Zsinocoso

↳ function ↳ odd function

{
even
cosz⊖ = cos 20 -
sin2⊖

^ ix. 4) 2<0520--1
I -
2sin2⊖
)⊖
>
1- ⊖

CX, -

y
✓




Graphs

or • @




6 • • •




v
↓
o 6 @




0 • @




>

, sets and logic
Week 2

* sets and logic NOT in calculus book

SETS

Basic concept of
•

a set.




•
count no .
elements in a set with finitely many elements .




•
understand what it means :




something is an element of a set


E symbol
when one set is a subset of another set

C
symbol
difference between something being an element of a set us .
subset of a set


Definition of intersection ( n) and union ( U)
•




•
An interval is a set of real numbers

•
Use of interval notation

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