ENGLISH MATH VIDEO TASK

Name : Noviana Serawati
NIM : 07305144030 Day, date : Monday, Des 01, 2008
Prodi : Math NR 07 Time :
E – mail : english.sera@gmail.com

English task on Tuesday, November 25, 2008
Class E room 204
Video 1
PRE CALCULUS

-- Graph of a rational function
Can have discontinuities has a polynomial in the denominator
Example:
f(x) = (x+3) /(x-1)
Is called Off Limit,when x = 1 subtitued to function f the denominator can be 0.
f(1) = 1+3/1-1
f(1) = 4/0
that’s impossible, the graph will shown break and discontinuity function.Bad choice.
When x = 0,

f(0) = 0+3 /0-1
f(0) = 3 /-1
f(0) = -3
That’s possible, not all rational function will give 0 in denominator and can be 0.

-- Break 2 ways in rational function:
1. Missing point is a loophole
Example:
y = (x^2+2x-3) / x-1
if x = 1 subtitued to function f
y = (1^2+2.1-3) /1-1
= 0/0
That’s not allowed, missing removable singularity when x leads to
The right way to solve that function with factor and simplify.
y = (x^2+2x-3) / x-1
y = (x-1)(x+3) / x-1
y = x + 3
Insert 1 to y = x + 3
y = 1 + 3 = 4 that’s no problem.
2. Zero in denominator
Example :
in function f(x) =(x+3) /(x-1) and insert 1.


Video 2
LIMIT by INSPECTION
1. x goes to positive or negative infinity
2. Limit involved a polynomial devided by a polynomial

Example 1:
Lim (x^3+7) /(x^2-x-6)
x--~
( polynomial over by polynomial with limit x approach infinity )
To solving limit above :
- looking the power of x in the numerator and denominator
- must be dividing f by polynomial if power of x in numerator highest than in denominator, limit can be positive or negative infinity
example above power of x in numerator highest than in denominator.

Example 2:
Lim (x+3) /(x^2-1)
x--~

Its mean power of x in denominator highest than in numerator, that limit will equal to 0.
Example 3 :
Lim (7x^3+x^2+1) / (3x^3+4)
x--~
That’s limit have same of power of x in denominator and in numerator, so the solution of that’s limit is same of the coefficient from the highest power of x in denominator and in numerator it self. The solution can be:
= Lim (7x^3+x^2+1) / (3x^3+4) = 7/3
x--~


Video 3
PROBLEM SOLVING ABOUT GRAPH MATH

-- The graph , if the function is difined by h(x)= g(2x)+ 2.What is the value of h(-1)?
Solution:
The fungtions is h(x)= g(2x)+ 2. If h(-1) is mean when x = -1, we substituted this to the functions
h(x)= g(2x)+ 2
h(-1)= g(2.0)+ 2
= g (-2) + 2
g(-2) is mean g when ,if we look the graph of y=g (x) we get g(-2)= 1 because x= -2 and y= 1
So h(-1)= g(-2)+ 2
= 1 + 2
= 3
We get the value of is 3.

-- Let the function f be defined by f(x)= 2x- 7 . If 4f(p)=24 ,What is the value of f(2p)?
Solution:
The function is f(x)= 2x- 7
The value of f(2p) is mean f when x= 2p ,we have 4f(p)= 24 because each space between have factors 4. So we can over by 4 and we get f(p)= 6
f(p)= 6 its mean f when x= p equal to 6, we can substituted this value to the function f(x)= 2x- 7 we get f(p)= 2p- 7= 6
2p = 13
p = 6,5
So we can get f(2p) If p = 6,5 so 2p = 13 is mean f when x=13 we subtitued this value to the function f(x)= 2x- 7
f(13)= 2.13- 7
= 26 - 7
= 19
We get the value of f(2p) is 19.

v In the xy coordinate x= y^2- 16 intersects line at (0,p) and (7,t) .What is the greatest possible value of the slope of l?
The function x= y^2- 16 intersects line at (0,p) and (7,t) .The formula of slope is m= (y2- y1) / x2- x1 the coordinate of l are (0,p) and (7,t) . thats mean x1= 0, y1= p, x2= 7, y2= t we subtitued thus to the m
m = (y2- y1) / x2- x1
= t- 0 / 7- p
= t / 7- p
We get the greatest possible value of the slope l is t / 7- p


Video 4
INVERS FUNCTION

Notation by : F(x,y) = 0
Function y = f (x) is called VLT and x = g (y) is called HLT

-- Function x = g(y) : invertible
Example:
1. Line function y = 4x – 3 and y = x
y = 4x – 3
x = 4x – 3
3 = 3x
x = 1
Subtuted x = 1 in y = 4x – 3
y =4 - 3 = 1
So, line function y = 4x – 3 and y = x intersect in (1,1)

4x – 3 = y
4x = y + 3
x = 1/4(y + 3)
x = 1/4 y + 3/4 and y = 1/4 x + 3/4

in invers function the line be write:
f(x) = 4x - 3
g(x) = 1/4 x + 3/4
f(g(x)) = 4(1/4 x + 3/4) -3
= x + 3 – 3
= x
g(f(x)) = 1/4(4x – 3) + 3/4
= x - 3/4 + 3/4
= x
From the operation above will get the conclusion :
g = f^-1
f(g(x)) = g(f^-1 (x)) = x
g(x) = f^-1 (f(x)) = x

2. Line function y= (x-2) /(x+3)
y(x+3) = x- 2
yx+ 3y = x- 2
(y-1)x = -2-3y
x= (-2- 3y) / (y- 1)
and
y= (-2- 3x) / (x-1)