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Math Help - Evaluating Limits Analytically

  1. #1
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    Evaluating Limits Analytically

    Hi, I'm new to the forum and this is my first post. Right now I'm trying to cram in limits, derivates, and application of derivatives in 2 weeks to prepare for next semester. I got credit for AP Calc AB so I'm only exempt from one semester of calculus.

    Anyways, I've been having trouble with the following problems, so I would appreciate if you guys could help out.

    Find the limit (if it exists).

    1) Limit as x tends to 2 for (X^3)-8
    X-2

    2) Limit as x tends to -4 (X+4)ln(X+6)
    (X^2)-16

    3) Limit as x tends to 0 Root(x+5) - Root(5)
    x

    4) Limit as x tends to 4 Root(X+5) -3
    X-4

    5) Limit as x tends to -3 from the left X
    Root X^2 - 9

    I've attempted the questions, but somehow got the answers of 1) DNE 2) ln2/-8 3) positive infinity 4) DNE

    Of course, my answers were wrong.

    Thank you!
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  2. #2
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    Quote Originally Posted by Mondy View Post
    Hi, I'm new to the forum and this is my first post. Right now I'm trying to cram in limits, derivates, and application of derivatives in 2 weeks to prepare for next semester. I got credit for AP Calc AB so I'm only exempt from one semester of calculus.

    Anyways, I've been having trouble with the following problems, so I would appreciate if you guys could help out.

    Find the limit (if it exists).

    1) Limit as x tends to 2 for (X^3)-8
    X-2

    Mr F says: Factorise the numerator and then cancel the common factor. Then take the limit.

    2) Limit as x tends to -4 (X+4)ln(X+6)
    (X^2)-16

    Mr F says: Factorise the denominator and then cancel the common factor. Then take the limit.

    3) Limit as x tends to 0 Root(x+5) - Root(5)
    x

    4) Limit as x tends to 4 Root(X+5) -3
    X-4

    5) Limit as x tends to -3 from the left X
    Root X^2 - 9 Mr F says: This expression is ambiguous. Please use appropriate brackets.

    I've attempted the questions, but somehow got the answers of 1) DNE 2) ln2/-8 3) positive infinity 4) DNE

    Of course, my answers were wrong.

    Thank you!
    3) Multiply numerator and denominator by \sqrt{x + 5} + \sqrt{5} and simplify: \frac{x}{x(\sqrt{x + 5} + \sqrt{5})}. Cancel the common factor and then take the limit.

    4) Done in a similar way.


    In future, please don't post more than two questions in a thread. Otherwise the thread can get convoluted and difficult to follow. Start new threads as necessary for remaining questions. eg. If you have five questions, post two of them in two threads and start a new thread for the remaining one etc.
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  3. #3
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    Quote Originally Posted by Mondy View Post
    Hi, I'm new to the forum and this is my first post. Right now I'm trying to cram in limits, derivates, and application of derivatives in 2 weeks to prepare for next semester. I got credit for AP Calc AB so I'm only exempt from one semester of calculus.

    Anyways, I've been having trouble with the following problems, so I would appreciate if you guys could help out.

    Find the limit (if it exists).

    1) Limit as x tends to 2 for (X^3)-8
    X-2
    If x \ne 2:

    \frac{x^3-8}{x-2}=\frac{(x-2)(x^2+2x+4)}{x-2}=x^2+3x+4

    CB
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Mondy View Post
    3) Limit as x tends to 0 Root(x+5) - Root(5)
    x
    Consider the limit of:

    \frac{\sqrt{x+5}-\sqrt{5}}{x}\times \left( \sqrt{x+5}+\sqrt{5} \right)

    Or use L'Hopital's rule.

    CB
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  5. #5
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    Quote Originally Posted by CaptainBlack and edited by MF View Post
    Consider the limit of:

    \frac{(\sqrt{x+5}-\sqrt{5})}{x}\times \frac{\left( \sqrt{x+5}+\sqrt{5} \right)}{\left( \sqrt{x+5}+\sqrt{5} \right)}

    Or use L'Hopital's rule.

    CB
    A small correction to the typo.
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by mr fantastic View Post
    A small correction to the typo.
    A typo it was not. Considering it the limit you will find padawan.

    CB
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