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Math Help - limits. please help

  1. #1
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    limits. please help

    Find the limits using first principle:
    1. lim (3x-1)5 (NB 5 is subscript)
    x -1

    2. lim x-2 (NB this is the square root of x -2)
    x4 x-4

    Find the limits algebraically:
    4. lim x-2
    x2 x3-8 (NB this is x cubed -8)

    5.lim ( x2 - 1 ) (NB this is x squared)
    x 1 x-1 x-1

    6.lim 1
    x 8- x-8

    7. lim 1
    x 8+ x-8

    8. lim 1
    x8 x-8
    Last edited by sade; September 24th 2007 at 06:21 PM. Reason: wrote wrong thing
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sade View Post
    Find the limits using first principle:
    1. lim (3x-1)5 (NB 5 is subscript)
    x -1
    I will assume you mean:

    <br />
\lim_{x \to -1} (3x-1)^5<br />

    (the 5 is a super-script).

    As (3x-1)^5 is continuous at x=-1 this limit is just (3x-1)^5 evaluated at x=-1.

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by sade View Post
    2. lim x-2 (NB this is the square root of x -2)
    x4 x-4
    As \sqrt{x-2} is continuous at x=4 this limit goes to \infty.

    Now if you mean:

    <br />
\frac{\sqrt{x}-2}{x-4}<br />

    we have a different problem which you solve by writting: x-4=(\sqrt{x}-2)(\sqrt{x}+2) for x \ge 0

    RonL
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  4. #4
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    Quote Originally Posted by sade View Post
    Find the limits using first principle:
    1. lim (3x-1)5 (NB 5 is subscript)
    x -1

    2. lim x-2 (NB this is the square root of x -2)
    x4 x-4

    Find the limits algebraically:
    4. lim x-2
    x2 x3-8 (NB this is x cubed -8)

    5.lim ( x2 - 1 ) (NB this is x squared)
    x 1 x-1 x-1

    6.lim 1
    x 8- x-8

    7. lim 1
    x 8+ x-8

    8. lim 1
    x8 x-8
    Did you have questions about when I helped you earlier? It would have been polite to ask me in that post, rather than double posting, which is against the rules.

    -Dan
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  5. #5
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    yes i would like to know how to do questions 5 - 8. i'm sorry about double posts. i'm new to this forum and i wasn't aware that what i was doing was against the rules
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