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Math Help - quick help

  1. #1
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    quick help

    i need help with starting this problem

    find the limit of the following as x---> 0

    [1/(x+1)]-1
    x
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by BigPapa View Post
    i need help with starting this problem

    find the limit of the following as x---> 0

    [1/(x+1)]-1
    x
    hard way (algebraic):

    not many algebraic options here, combine the fractions in the numerator, you get:

    \lim_{x \to 0} \frac {\frac {-x}{x + 1}}x

    now what?

    "easy" way: realize that this is the derivative of \frac 1x at x = 1. (of course, the x here would usually be "h" in the formula, but that doesn't matter)
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    hard way (algebraic):

    not many algebraic options here, combine the fractions in the numerator, you get:

    \lim_{x \to 0} \frac {\frac {-x}{x + 1}}x
    well we havent gotten to derivatives yet so i have to do it algebraicly
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by BigPapa View Post
    well we havent gotten to derivatives yet so i have to do it algebraicly
    ok, so finish up. how can you simplify where i left off?
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  5. #5
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    ok i think i got it.

    from there you multiply the numerator by 1/x and you end up with

    -x
    x(x+1)

    x's cancel

    -1
    (x+1)

    substitute 0 for x and you get

    -1

    (sorry i dont know how to do the math codes or anything. i just have to use the underline and stuff lol)
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by BigPapa View Post
    ok i think i got it.

    from there you multiply the numerator by 1/x and you end up with

    -x
    x(x+1)

    x's cancel

    -1
    (x+1)

    substitute 0 for x and you get

    -1
    that is correct

    (sorry i dont know how to do the math codes or anything. i just have to use the underline and stuff lol)
    no worries.

    if you are so inclined, you can learn the codes here

    if not, just type fractions thusly:

    (numerator)/(denominator)

    example, you would type your second to last line as (-1)/(x + 1), or simply -1/(x + 1) since there is no ambiguity there.

    but please use parentheses wisely. if you had typed -1/x + 1 that would be wrong!
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  7. #7
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    ok thanks for your help. i think i might go learn the codes
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