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Math Help - Determine the end behavior of each function...?

  1. #1
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    Determine the end behavior of each function...?

    a) f(x) = 17 + 3x^2 - 13x^3 - 6x^4

    b) f(x) = (5x^2-7x+2)/(4x^2-2)

    c) e^x

    all of them are asking for two answers. the first as x to -infinity and the second as x to infinity.

    thank you thank you =)
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  2. #2
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    Quote Originally Posted by melliep View Post
    a) f(x) = 17 + 3x^2 - 13x^3 - 6x^4

    b) f(x) = (5x^2-7x+2)/(4x^2-2)

    c) e^x

    all of them are asking for two answers. the first as x to -infinity and the second as x to infinity.

    thank you thank you =)
    Have you done these kinds of limits before?

    a) Which term dominates the others as x approaches +/- infinity?

    b) Which term in denominator dominates, which term in numerator..?

    c) If it's not obvious.. which I guess it's not since you're asking.. just graph it. Then justify it.
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  3. #3
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    Quote Originally Posted by melliep View Post
    a) f(x) = 17 + 3x^2 - 13x^3 - 6x^4

    b) f(x) = (5x^2-7x+2)/(4x^2-2)

    c) e^x

    all of them are asking for two answers. the first as x to -infinity and the second as x to infinity.

    thank you thank you =)
    b) You could also do a polynomial long division to get \displaystyle f(x) = \frac{-7x+\frac{9}{2}}{4x^2 - 2} + \frac{5}{4} ....
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  4. #4
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    mmm I'm really sorry that doesn't help me.
    I've never learned this before and I'm expected to since I'm in adv. calc.
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  5. #5
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    Yet another way to handle (b) is

    (x won't be 0)

    \displaystyle \frac{5x^2-7x+2}{4x^2-2}=\frac{\frac{1}{x^2}(5x^2-7x+2)}{\frac{1}{x^2}(4x^2-2)}=\frac{5-\frac{7}{x}+\frac{2}{x^2}}{4-\frac{2}{x^2}}
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  6. #6
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    Quote Originally Posted by melliep View Post
    mmm I'm really sorry that doesn't help me.
    I've never learned this before and I'm expected to since I'm in adv. calc.
    This might help, I found it w/ google search and seems good at a glance

    Limits to Infinity
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  7. #7
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    Quote Originally Posted by melliep View Post
    mmm I'm really sorry that doesn't help me.
    I've never learned this before and I'm expected to since I'm in adv. calc.
    Sorry to ask, but how did you get into an advanced calculus class without having the necessary mathematical pre-requisites?
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  8. #8
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    Hahaha...thanks...
    Mmm because I'm smart, maybe?
    And because I'm good at taking tests.
    Sorry if my question was not up to par.
    Thanks for your help.
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