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  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#1 Re: Help Me ! » limit problem » 2006-11-01 01:56:58

what a great job Dross !

Is there any other way to prove without using the epsilon - delta defenition!? .

#2 Help Me ! » limit problem » 2006-10-30 19:36:34

mahmoudaljamel
Replies: 3

f(x) =X² if x is rational , 0 if x is irrational


             Prove that lim f(x) as x approaches 0 is equel to 0

#3 Re: Help Me ! » simplify......Help » 2006-10-30 04:15:33

No , you use the C in your question , then you ignore it in the firest step of solution ,
you should end up with :


   ( CB + x ) / (CB + X + B )

#4 Re: Help Me ! » Largest integer function ! » 2006-10-30 03:59:01

Thanks for the very fruitful discussion; I would like to put the following notes:
 
  1.  The lim of f(x) as x approaches n is equal to f(n) if f(n) is defined , this statement should be changed to : if n is in the domain of f(x).

2. [x] = - [-x] if x is integer only

3. very interested to be introduced to the idea of flooring and ceiling , since I  never see it in the American books

#5 Re: Help Me ! » Largest integer function ! » 2006-10-29 03:39:05

Dross

the squar brackets stands for " largest integer number less than or equal x "
this is the notation used in the books, to refresh the memories of all members, these are examples : [1.5] = 1 , [4.3] = 4 , [-2.1] = -3

#6 Help Me ! » Largest integer function ! » 2006-10-28 20:55:35

mahmoudaljamel
Replies: 15

f(x) = [ x ] + [ - x ]

       proove that lim of f(x) as x approaches 2 , exicts and is not equal to f(2)

#7 Re: Help Me ! » Help me on functions pls.. » 2006-10-28 20:09:54

1. ( f - g ) (x)
  Normal subtraction as the subtraction of numbers
    ( f - g ) (x) = (5 + 2/x) - (x-1)
                     = 5 + 2/x -x + 1
                     = 6 + ( 2-x²)/x
    ( f - g ) (1) = 7

2. ( f o g ) (x) = f ( g (x) )
                     = f ( x-1)
                     = 5 + 2 / ( x-1)
   
    ( f o g ) (2) = 7

3. f-¹ (x)  :

               y = 5 + 2/x
            y-5 =2/x
       x (y-5) = 2
               x = 2 / ( y-5 )

#8 Re: Help Me ! » Algebra is *too* hard.. » 2006-10-19 07:34:34

Hi
I strongly believe that doing "good" in maths is a matter of love !!
if u love ALGEBRA u'll do "good"
I believe also that loving maths is not related to the material itself!!, in someway its related to the atmospher surrounding it , the teacher is the first and most important factor

To solve ur problem , take these advises:

1. Don't tel urself that u have a bad relation with algebra and u will never reach the right answer...tell urself always and laudly that ur good and algebra is a nice friend

2. Start from the zero level and memorize all the definitions and rules in ur way , u can use this site to start with 

3. Always use ur pencile and papers in solving a problem , don't rely on ur eyes alone.

4. whenever u have a wrong answer , go back and solve a gain after knowing the right answer.

#9 Re: Help Me ! » matchstick puzzle HELP » 2006-10-09 20:55:06

If we move one of the sticks from the group of 3(III) and place it with the single stick (I):

II + II + II = IIII

we have 6 sticks on the left side , while we have 4 sticks on the other 

So ..
polylog solution is wrong

Let me suggest this idea:

I + (II) + III = IIII
I + (+) + III = IIII

Converting the (II) into (+) , will give  1 + 3 = 4

#10 Re: Help Me ! » digits » 2006-10-09 20:27:00

1000a + b = 3ab
1000a - 3ab = -b
a( 1000 - 3b) = -b
a ( 3b - 1000) = b

a = b / ( 3b - 1000)

#11 Re: Puzzles and Games » The Prisoners and the Lightbulb » 2006-09-23 20:11:55

If we assign a man to say : i want to go back to earth , he can say that after he is taken to the central room the second time.
since the time is not important for them , then this is an acceptable  solution based on Dross hint.

#12 Re: Puzzles and Games » Rectangle !! » 2006-09-23 19:41:53

This is a question found in a " pre calculus " book , the authers put 80 m and 60 m as the answers , i could reach one equation in two variables , but never come to a second equation .
Now , if we know that the answer should be 60 m and 80 m , can we work back to find any new equation !!
thanks Dross
thanks mathsyperson

#13 Re: Puzzles and Games » The Prisoners and the Lightbulb » 2006-09-20 22:15:51

No chance , they will be killed all !!
Dross :
give us time to think , please

#14 Puzzles and Games » Rectangle !! » 2006-09-20 22:08:26

mahmoudaljamel
Replies: 6

The length of a rectangle was increased by 10 m , the width was increased by 5m ,
as a result the area was increased by 1050 m².
Find the original lenth and width

#15 Re: Help Me ! » derivatives problems » 2006-09-17 19:45:40

f(x) = 1/ ( x+2)½
      = ( x+ 2)- ½
f'(x)= [-1/2 ( x+2 )- ³/ ² ]* 1
      = -1 / [ 2 (x+2)³/ ²]
f'(a)= -1 / [2 (a+2)³/ ² ]
f'(2)= -1 / [2 (4)³/ ²]
      = -1 / 16

can you please rewrite the second question
hmm

#16 Re: Help Me ! » cost price » 2006-09-17 04:56:43

Sorry to say that HOOYOO solution is wrong ,
solving the two equations given by HOOYOO will give x= 1112.76, y = 1767.24 but
if we check by multiplying x and y by 1.2 it will not sum up to 3000.

this is my solution :

Let x the cost of table and y the cost of chair

he sold the table and the chair at 3000 and made 20% profit
(x + y)*1.2 = 3000
x + y = 2500
2500 is the cost of both table and chair
if he sells the chair at cost and the table at 1800 , he would make 12 %
y + 1800 = (2500 * 1.12)
y + 1800 = 2800
y = 1000
1000 is the cost of chair
x = 2500 - 1000 = 1500
1500 is the cost of table

#18 Re: Help Me ! » find an equation.. » 2006-09-12 22:43:03

hi ,
for a line passing through (x1,y1) and (x2,y2) , use this equation :
m (slope) = (y2-y1)/(x2-x1)
y-y1 = m(x-x1)
in our case :
m= 24-2 / 12-1 = 22/11 = 2
y - 2 = 2 ( x- 1)
y - 2 = 2x-2
y = 2x

For the circle :
The equation used is the standard equation that has the form

(x - h)² + (y - k)² = r2
where h and k are the x- and y-coordinates of the center of the circle and r is the radius.
( x-3)[sup]2[/sup] + ( y-3)[sup]2[/sup] = 81

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