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Math Help - Limits

  1. #1
    Member Mr Rayon's Avatar
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    Limits

    hi guys,

    Just started the topic on limits. I was just wondering whether somebody could help me go through the following questions.

    Evaluate the following limits:

    (a) \lim_{x\rightarrow \infty } \frac{2x(x^2-1)}{x^2(5x-4)}

    (b) \lim_{x\rightarrow \infty } \frac{x^3}{2x^2+7}

    (c) \lim_{x\rightarrow -\infty } \frac{2x-1}{x^4+3x+1}

    Any help would be appreciated!
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  2. #2
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    Re: Limits

    Have you worked on these questions. Please post the effort made.
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  3. #3
    Member Mr Rayon's Avatar
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    Re: Limits

    Quote Originally Posted by ibdutt View Post
    Have you worked on these questions. Please post the effort made.
    a) as the highest powers in both the numerator and denominator are the same when expanded, the limit is just the coefficients of the highest powers in the numerator and denominator.
    So, 2/10 which simplifies to 1/5.

    b) as the numerator's highest power is greater than the denominator's highest power - the limit does not exist.

    c) as the numerator's power is lower than the denominator's power, the limit is equal to 0.


    ??

    Is this correct?

    Please get back to me!
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  4. #4
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    Re: Limits

    You can verify by dividing the numerator and denominator by the highest power of the variable.
    Q 1. it is x^3. On dividing the numerator and the denominator by x^3 we get [2 - 2/x^2 ] / [ 5 - 4/x] the limit of this as x approaches infinity is 2/5
    Similarly you can find the limits of other questions.
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  5. #5
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    Re: Limits

    Quote Originally Posted by Mr Rayon View Post
    a) as the highest powers in both the numerator and denominator are the same when expanded, the limit is just the coefficients of the highest powers in the numerator and denominator.
    So, 2/10 which simplifies to 1/5.

    b) as the numerator's highest power is greater than the denominator's highest power - the limit does not exist.

    c) as the numerator's power is lower than the denominator's power, the limit is equal to 0.


    ??

    Is this correct?

    Please get back to me!
    a and c is correct. b is incorrect
    Divide your b by x^2 in top and bottom
    Regards,
    Last edited by Petrus; April 12th 2013 at 08:43 AM.
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