THE VIDEOS

1. Pre Calculus Graph
Let’s begin by discussing the graph of a rational function which can have discontinuities. A rational function has a polynomial in the denominator which means you are dividing by something that is valuable quantity.
It’s possible that some value of x will meet to division be zero. Example:
If f(x)=(x+2)/(x-1), when x=1, the function value become f(x)=(1+2)/(1-1)=3/0 with 0 in the denominator. For this function, choosing x=1 is a bad idea.
When there is a bad choice of x when it makes the bottom of the rational function, it shows up a break in a function graph. For example, suppose you to finding the graph f(x)=(x+2)/(x-1). Start with inserting 0 for x. So now we have f(0)=(0+2)/(0-1)=2/(-1)=-1. So, you put off point down on the graph at (0,-2).

Next you try x=1. This time you get f(1)=(1+2)/(1-1)=3/0. That is you know is impossible and it means that you can not compute y-value when x=1.
It also mean that the graph of this function will not have any point for x=1. The graph is separated into two disconnected pieces at x=1.

Take the graph of f(x)=1/(x^2+1). No matter what numbers you choose for x, the denominator will never zero. The graph is smooth and unbroken.

Don’t forget that the general rule on the rational function, you must expect the possibility that the denominator may turn out to be zero.
Review: For polynomials, the graph is a smooth unbroken curve. For a rational function, sometimes the value of x may be zero in the denominator. That is an impossible situation because there is no y for that x. At that point, there is no value for the function and there is a break in the graph.
A break can show up in two ways. The simpler type of a break is just a missing point. This function is an example of this type of break: y=(x^2-x-6)/(x-3).

The gate that appear in the graph is at points where x=3. If you try to substitute 3 for x in the equation, the result is y=(3^2-3-6)/(3-3)=0/0. That is not possible, not feasible, and not allowed. So, there is no y for x=3. That is the typical example of the missing point syndrome and conveniently it always goes with the result like 0/0.
When you see the result of 0/0, it also tells you that it should be possible to factor the top and the bottom of the rational function and simplify. For an example: y=(x^2-x-6)/(x-3)=(x-3)(x-2)/(x-3)=(x+2).
For this kind of the break, the missing point is a loop hole. For the original function without simplify, x=3 is a bad point because it leads to the division be zero, y=0/0. But if you simplify first, then there’s no problem with x=3, y=x+2. It can be one idea or key in calculus.
Removable singularity appears simplest missing points on the graph when x leads to 0/0. For this kind of a break, if you factor and simplify the rational function, the division by zero can be avoided.

2. Kata Kerja

Kata kerja menunjukan sebuah kegiatan atau untuk menjelaskan sebuah kejadian. Tentang apa yang sedang dilakukan oleh suatu kalimat.
Dalam sebuah kalimat sederhana:
Dave berlari
Kata kerja
Karena berlari menunjukan apa yang sedang dilakukan Dave.
Dalam tata Bahasa Inggris, perubahan bentuk kata kerja menunjukan siapa yang sedang melakukan kegiatan tersebut.
I do, you do, he does, we do, they do.
Contoh : Dave runs, tetapi kita mengatakan I run
Kata kerja berubah karena orang lain yang nelakukan kegiatan tersebut
I, You, We, They He, She, it

run runs
kata kerja - to be
I am
You are singular sbyek/kata ganti tunggal, diikuti kata kerja tunggal
She is
It is
We are
They are kata ganti jamak, diikuti kata kerja jamak
Contoh :
Nyonya Midori adalah kata ganti tunggal, jadi menggunakan :
Mrs Midori Yodels bentuk yang digunakan untuk kata ganti tunggal.
Saudara-saudara Midori seperti Else, Gretel, Heidi. Mereka adalah kata ganti jamak, maka menggunakan kata kerja jamak :
Midori’s sister yodel.


3. Basic Trigonometry
Trigonometry (from g reek, trigon and metron). Trigonometry is relly study of rectangle and the relationship between the side and the angle of rectangle.

Function
Sin Ǿ = ?
cos Ǿ = ?
tan Ǿ = ?
to solve them, use triy function soh, cah, toa.
Soh : sine is opposite over hypotenuse
Cah : cosine is adjacent over hypotenuse
Toa : tangent is opposite over adjacent

- Sin Ǿ = 4/5 the other trigfunctions : 1. Cosecant Ǿ

- Cos Ǿ = 3/5 2. Secant Ǿ

- Tan Ǿ = 4/3 3. Catangent Ǿ

If the angle is x, so tan x = ¾ (the invers of tan Ǿ)

4. Kalimat Majemuk

Contoh :
Klausa 1 : It’s the end of the world as we know it, and
Klausa 2 : I feel fine
Ada 2 klausa yang dihubungkan dengan 1 kata penghubung, yaitu “and” ketika satu kalimat digunakan sebagai bagian dalam kelompok yang lebih besar, kalimat yang lebih kecil disebut klausa.
Ketika sebuah klausa dpaat berdiri sendiri dalam sebuah kalimat, maka disebut “independent clause”. Jika memiliki 2 klausa, maka disebut dengan kalimat majemuk. Untuk menggabungkan 2 independent klausa menggunakan tanda titik dua (:), klausa yang kedua menjelaskan klausa yang pertama.
- I love my two sisters. They bake me pie.
Untuk menggabungkan kedua kalimat tersebut, menggunakan tanda titik dua
- I Love my two sister : they bake me pie
• Tanda titik koma (;)
Contoh kalimat :
It’s the end of the world as we know it and I feel fine
Dapat disingkat menjadi :
It’s the end of the world as we know it, I Feel fine.
• Garis penghubung (-)
Terdiri dari beberapa elemen yang mengejutkan. Kita menggunakan garis penghubung karena klausa kedua dihubungkan dengan klausa pertama
Untuk menghubungkan kalimat terdapat 4 cara :
- Kata penguhubung
- Titik dua
- Titik koma
- Garis penghubung
• Kalimat Fragmen
Jika kita mendapati suatu kalimat tidak dapat berdiri sendiri sebagai kalimat lengkap. Contoh kalimat lengkap:
My pet Komodo dragon is a lamb
Contoh kalimat fragmen :
Because he has no teeth
Klausa dependent : - tidak bisa berdiri sendiri
- klausa dependent terdapat pada klausa independent
- bukan kalimat lengkap
Contoh :
Although Tom sleeps regulary, he is constantly tired
Klausa dependent klausa independent
Kalimat diatas disebut kalimat kompleks.

5. Limit By Inspection

There are two conditions :
1. X goes to positive or negative infinity
2. Limit involves a polynomial divide by a polynomial
For example :
Lim x3 + 4 = ~
x2 + x+1
X→ ~
(Because highest power of x in number is 3 greater than highest power in denominator) since all the number are positive and x is positive infinity
The key to defermining limits by inspection is in looking at powers of x in the numerator ana the denominator. To apply these rules : - must be divining by polynomial
- x has to be approaching infinity

1. First shortcut rule
If the highest power of x in numerator is 3 greather than highest power in denominator) since all the number are positive and x is going to positive infinity if you can’t tell it the answer is positive or negative:
- substitute a large number for x
- see if you end up with a positive or negative number
- whatever sign you get is the sign of infinity for the limit.

2. Second shortcut rule:
If the highest power of x is in the denominator, then limit is zero
Lim x2 + 3
x → ~ x3 + I , x2 + 3 = highest power of x in numerator is 2
x3 + 1 = highest power of x in denominator is 3

3. Last shortcut rule
Used when : highest power of x in numerator is same as highest power of x in denominator.
Lim = the quotient on the efficient on the two highest powers
x → ~
-Remember : coefisient → the number that goes with a variable
Ex : 2 is the coefficient of 2x2
75 is the coefficient of 75 x 4
Sho that is no way if x = 3

When you see the result and also tell you direction be possible factor top and bottom of rasional function and simplify

6. Trig Function

Trig function : really study of right triangle

To remember you can use : s o h c a h t o a
i p y o d y a p d
n p p s j p n p j
e o o i a g
s t n c e
i e e e n
t n n t
u t
s
e
Trig Function
- ratios of different sides of triangles
- With respect to an angle
- Only need to know values of sides to find measure of an angles figure of all part of triangle
Trig function : 1. Sine 4. Cosecant
2. cosine 5. Secant
3. tangent 6. cotangent


Six basis trig function defined by :
1. Sides of a triangle
2. angle being measured
opp : side opposite to theta
adj : side adjacent to theta
hyp : hypotenuse
Six trig function : 1. Sin Ө 3. Tan Ө 5. secӨ
2. cos Ө 4. Csc Ө 6. Cot Ө
Trid shortcut

According to this rule :
Lim → coefficients of x³ is over cach other
Lim
x 4

7. Kalimat Sederhana

Kebanyakan tipe kalimat adalah kalimat sederhana, sederhana karena semua elemen didalam kalimat adalah bagian dari subjek dan predikat. Subjek menunjukan kegiatan dari kata kerja utama. Subjek sederhana adalah kata benda khusus yang menunjukan sebuah kegiatan.
The happy little child kicked the gnome over the fence
Subyek
Predikat dari sebuah kalimat terdiri dari : main verb kata kerja utama dan apapun yang mengikutinya. Gabungan keduanya disebut predikat yang lengkap. Contoh :
The happy little child kicked the gnme over the fence predikat yang lengkap.
Karena “kecked the gnome over the fence” menunjukan tentang apa yang ditendang dan bagaimana tendangan itu secara lebih jelas lag.
- Kalimat sederhana dapat diperoleh tanpa subjek dan predikat.
- Kalimat perintah adalah kalimat yang ditunjukan langsung kepada orang kedua, yaitu “kamu”, berfungsi untuk memerintahkan seseorang agar melakukan sesuatu.
Kick that gnome over the fence
- Tidak ada subjek
- Siapa yang sebenarnya melakukan kegiatan tersebut?”kamu”
Bisa ditulis : “Hey you, kick that gnome over the fence.”
Tidak perlu ditulis karena sudah tersirat