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    Limits

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    Justice
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    Limits

    Post by Justice on Fri Sep 17, 2010 7:26 pm

    Ok so this is how you would do limits....

    Lim (x^3+8 )/(x^2-4)
    x->-2

    Lim (√(1+3x^4)-√(1-2x))/(x+x^2+2 x^3 )
    x->0


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    Re: Limits

    Post by Ahmed on Fri Sep 17, 2010 7:32 pm

    The first has no limit.

    The second is 0 (zero).


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    Re: Limits

    Post by Justice on Fri Sep 17, 2010 7:44 pm

    So what is a limit? A limit is when a function approaches a certain number. Thus i am asking what happens to the function when (x^3+8 )/(x^2-4) approaches -2.
    Thus...
    ((x)^3+(2)^3)/(x-2)(x+2)
    ((x+2)(x^2+x+4))/(x-2)(x+2)
    (x^2+x+4))/(x-2)
    now Plug in -2 and you will get your answer


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    Re: Limits

    Post by Ahmed on Fri Sep 17, 2010 7:47 pm

    So all I had to do was simplify it first?


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    Re: Limits

    Post by Justice on Fri Sep 17, 2010 7:50 pm

    Exactly! And it is much faster then making a graph.
    Warning: Usually in algebra you CAN NOT divide by variables but since we are doing limits we can


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    Re: Limits

    Post by Ahmed on Fri Sep 17, 2010 7:51 pm

    Well how do you know if something is not a limit?


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    Re: Limits

    Post by Ahmed on Fri Sep 17, 2010 8:00 pm

    -1.5 is the limit for the first one.


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    Re: Limits

    Post by Justice on Fri Sep 17, 2010 8:04 pm

    Every function has a limit. Only if the limit approces infinity it can have no limit. (I need to check though)
    And congratz you can plug in numbers!


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    Re: Limits

    Post by Ahmed on Fri Sep 17, 2010 8:09 pm

    Wrong! A function is not a limit if it approaches infinity or if it goes in two directions.


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    Re: Limits

    Post by Justice on Fri Sep 17, 2010 8:09 pm

    the lim x->0 sin(1/x) is an example cause it has to many wiggles


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    Re: Limits

    Post by Ahmed on Fri Sep 17, 2010 8:11 pm

    No man...forget sin, cos tan. Just use normal ones.


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    Re: Limits

    Post by Justice on Fri Sep 17, 2010 8:25 pm

    (√(1+3x^4 )-√(1-2x))/(x+x^2+2 x^3 )*(√(1+3x^4 )+√(1-2x))/(√(1+3x^4 )-√(1-2x)
    Simply further


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    Re: Limits

    Post by Ahmed on Fri Sep 17, 2010 8:37 pm

    Oh I see...multiplying by the conjugate.


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    Re: Limits

    Post by Ahmed on Sat Sep 18, 2010 2:22 pm

    Lev what book are you using to study AP Cal?


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    Re: Limits

    Post by Justice on Sat Sep 18, 2010 3:55 pm

    Im first gona do all of Khan's videos. then i will just do review books.


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    Re: Limits

    Post by Ahmed on Sat Sep 18, 2010 3:56 pm

    Post links to khans videos here


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    Re: Limits

    Post by Justice on Sat Sep 18, 2010 4:33 pm



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    Re: Limits

    Post by Ahmed on Sat Sep 18, 2010 4:35 pm

    Wow...so many vids O.O'!


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    Re: Limits

    Post by Doc on Sat Sep 18, 2010 5:32 pm

    tell me when u learn lhospitals rule
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    Re: Limits

    Post by Ahmed on Sat Sep 18, 2010 5:39 pm

    Sure. But could you teach me limits first lol?


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    Re: Limits

    Post by Doc on Sat Sep 18, 2010 5:44 pm

    dude i suck at life ... i got a A- in calc
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    Re: Limits

    Post by Ahmed on Sat Sep 18, 2010 5:49 pm

    That's pretty good bro. And limits is the first topic in cal. So...help?


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