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Math Help - Calculus - Infinite Limits and Asymptotes (Several Problems)

  1. #1
    Member FalconPUNCH!'s Avatar
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    Calculus - Infinite Limits and Asymptotes (Several Problems)

    Hi I just need help with several problems. I worked them out and I got an answer but I'm not sure if I did it correctly. Please check my answers.

    Problem 1
    Find the Limit:

    Lim as X -> Positive Infinity of T^2 + 2/ T^3 + ^2 - 1

    I don't want to put all my work because I don't know the shorthand to doing it and I'll just put the answer I got. I got 0 as the limit to this problem.


    Problem 2
    Find the Horizontal and Vertical Asymptotes of each curve:

    Y = 1 + X^4/X^2-X^4

    I got Horizontal = -1 and Vertical = 1, -1

    Problem 3
    Same as above


    Y = 2e^x/e^x-5

    I got Horizontal = 0 and Vertical = -1

    Problem 4
    Find the limit


    Lim x-> positive infinity COSX

    I got Lim doesn't exist because COSX is a periodic.
    Last edited by FalconPUNCH!; October 7th 2007 at 09:48 PM.
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  2. #2
    Member FalconPUNCH!'s Avatar
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    Okay I changed some of my answers. I think they're all right but I just need someone to double check for me.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by FalconPUNCH! View Post
    Hi I just need help with several problems. I worked them out and I got an answer but I'm not sure if I did it correctly. Please check my answers.

    Problem 1
    Find the Limit:

    Lim as X -> Positive Infinity of T^2 + 2/ T^3 + ^2 - 1

    I don't want to put all my work because I don't know the shorthand to doing it and I'll just put the answer I got. I got 0 as the limit to this problem.
    did you mean \lim_{T \to \infty} \frac {T^2 + 2}{T^3 + T^2 - 1}? if so, you are correct


    Problem 2
    Find the Horizontal and Vertical Asymptotes of each curve:

    Y = 1 + X^4/X^2-X^4

    I got Horizontal = -1 and Vertical = 1, -1
    i suppose you mean y = \frac {1 + x^4}{x^2 - x^4} (you should use parentheses).

    your horizontal asymptote is fine. as for you vertical asymptotes, what about x = 0?


    Problem 3
    Same as above


    Y = 2e^x/e^x-5

    I got Horizontal = 0 and Vertical = -1
    your vertical asymptote is wrong. remember, you want e^x - 5 = 0

    for the horizontal, you forgot y = 2. remember you have to take two infinite limits here, \lim_{x \to \infty}f(x) and \lim_{x \to - \infty}f(x)


    Problem 4
    Find the limit


    Lim x-> positive infinity COSX

    I got Lim doesn't exist because COSX is a periodic.
    correct, it "oscillates"
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  4. #4
    Member FalconPUNCH!'s Avatar
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    Quote Originally Posted by Jhevon View Post
    did you mean \lim_{T \to \infty} \frac {T^2 + 2}{T^3 + T^2 - 1}? if so, you are correct


    i suppose you mean y = \frac {1 + x^4}{x^2 - x^4} (you should use parentheses).

    your horizontal asymptote is fine. as for you vertical asymptotes, what about x = 0?

    your vertical asymptote is wrong. remember, you want e^x - 5 = 0

    for the horizontal, you forgot y = 2. remember you have to take two infinite limits here, \lim_{x \to \infty}f(x) and \lim_{x \to - \infty}f(x)

    correct, it "oscillates"
    Wow thank you a lot. Yeah I think i should have use parenthesis to make myself more clear. You're the best Jhevon
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by FalconPUNCH! View Post
    Wow thank you a lot. Yeah I think i should have use parenthesis to make myself more clear.
    you're welcome. and yes, parentheses are important.
    You're the best Jhevon
    not really. i let you wait for over an hour for questions i could have answered in less than a minute. sorry about that. i should treat users who attempt their own questions with more respect. good luck, you seem to know your stuff for the most part. just remember, for horizontal asymptotes, you take two infinite limits, one as we go to infinity, one as we go to -infinity. and we have vertical asymptotes for a rational function everywhere the denominator is zero
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  6. #6
    Member FalconPUNCH!'s Avatar
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    Quote Originally Posted by Jhevon View Post
    you're welcome. and yes, parentheses are important. not really. i let you wait for over an hour for questions i could have answered in less than a minute. sorry about that. i should treat users who attempt their own questions with more respect. good luck, you seem to know your stuff for the most part. just remember, for horizontal asymptotes, you take two infinite limits, one as we go to infinity, one as we go to -infinity. and we have vertical asymptotes for a rational function everywhere the denominator is zero
    Yeah my professor didn't tell us how to find the asymptotes so I tried to the best of my knowledge. Thanks again.
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