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I confronted something in math which is way too confusing to me

  1. Jan 27, 2012 #1
    I confronted "something" in math which is way too confusing to me !!

    Hello forums ,
    I am currently in class 10th , and 15 years... I was doing Khan Academy Pre-calculus yesterday and I confronted something too weird ... not weird though but way too confusing...
    :cry:

    Here is the link :
    http://www.khanacademy.org/video/more-limits?playlist=Precalculus [Broken]

    Now what I am confused with , is that , Sal ( That's not a name of a tree !) says that

    lim (x-2|x|)/|x|
    x→0

    Then he says that when limit x tends to 0 from positive side then :

    lim (x-2|x|)/|x|
    x→0+

    is SAME AS

    lim (x-2x)/x
    x→0+

    which is equal to

    lim (x-2|x|)/|x| = -1
    x→0+

    This makes sense to me and here comes which confuses me :

    Now Sal says that when x approaches 0 from negative side then :

    lim (x-2|x|)/|x|
    x→0-

    is SAME AS

    lim (x-2(-x))/-x
    x→0-

    which is equal to

    lim (3x)/-x
    x→0-

    SO

    lim (x-2|x|)/|x| = -3
    x→0-

    This does not make sense ! |-x| → |x| right ?
    Why he wrote |-x| = -x ?! OR |x| = -x ? ! where x < 0 ?!

    Can someone explain it to me , please ?:frown:

    Thanks in advance ...:smile:
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jan 27, 2012 #2
    Re: I confronted "something" in math which is way too confusing to me !!

    |x| is the absolute value of x, so you "ignore the minus sign". For positive number, an example would be say, |5|=5. So you can see that |x|=x if x > 0. For negative x, say -3, its absolute value is |-3|=3, yes? But 3=-(-3), so |x|= -x if x < 0.
     
  4. Jan 27, 2012 #3

    jedishrfu

    Staff: Mentor

    Re: I confronted "something" in math which is way too confusing to me !!

    As Yenchin says you can't work with |x| directly and so you break the problem up into two cases:
    - one equation where x is positive so that you can replace |x| with x
    - one equation where x is negative so that you can replace |x| with -x

    these replacements come from the definition of the absolute value function:
    - for x>0 the value is x
    - for x=0 the value is 0
    - for x<0 then value is -x

    and since x=0 can't be used due to division by zero being an undefined operation.
     
  5. Jan 27, 2012 #4
    Re: I confronted "something" in math which is way too confusing to me !!

    Thanks yenchin and jedishrfu !
    Now I know why Sal wrote |x| = -x , where x<0 !
    You two mean that here x < 0 and so x is negative.
    So -x will here be positive i.e. -x>0 or x<0
    As we know that "absolute function || " yields positive value , so |x| = -x where x<0
    AND
    |x| = x , where x>0
    AND
    |-x| = x , where x>0
    AND
    |-x| = -x , where x<0 , in number form I write it like -: x=-1
    |-(-1)| = |1| = 1 which is same as -x right ?
    Is this what you two mean right ?

    Now I can move forward in pre-calculus.

    Thanks a lot ! :smile:
     
  6. Jan 27, 2012 #5

    Mark44

    Staff: Mentor

    Re: I confronted "something" in math which is way too confusing to me !!

    What you have above is sort of the definition of the absolute value. In a briefer form, it is:
    |x| = x, if x >= 0
    |x| = -x, if x < 0
     
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