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Math Help - Limit: Describing Behavior

  1. #1
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    Limit: Describing Behavior

    This was just on the calculus board, but that was 4 hours ago with 3 views. Now, its urgent.

    Hallo to everyone!

    Describe the behavior of f(x) to the left and right of each vertical asymptote.

    f(x) = tan x/ sin x







    Are (0, 8 ) and (0,-8 ) at least starting points?


    The answer is the book says:
    a= (4k + 1) pi/2
    b= (4k+ 4) pi/2

    I have no clue what they are talking about.
    The only helpful thing in the book is the definition of a vertical asymptote:

    The line x= a is a vertical asymptote of the graph of a function y= f(x) if either
    lim as x--> a+ f(x) = +/- infinity
    lim as x--> a- f(x) = +/- infinity

    I'm really lost.

    Does AP Calculus questions go on this board?

    Thanks.
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  2. #2
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    Quote Originally Posted by Truthbetold View Post
    This was just on the calculus board, but that was 4 hours ago with 3 views. Now, its urgent.

    Hallo to everyone!

    Describe the behavior of f(x) to the left and right of each vertical asymptote.

    f(x) = tan x/ sin x







    Are (0, 8 ) and (0,-8 ) at least starting points?


    The answer is the book says:
    a= (4k + 1) pi/2
    b= (4k+ 4) pi/2

    I have no clue what they are talking about.
    The only helpful thing in the book is the definition of a vertical asymptote:

    The line x= a is a vertical asymptote of the graph of a function y= f(x) if either
    lim as x--> a+ f(x) = +/- infinity
    lim as x--> a- f(x) = +/- infinity

    I'm really lost.

    Does AP Calculus questions go on this board?

    Thanks.
    Maybe your question wasn't answered because it makes no sense. It looks to me more like you are to find the position of the asymptotes? But what are a and b supposed to be?

    Anyway, to find the asymptotes we look for where the denominator of the function is 0:
    f(x) = \frac{tan(x)}{sin(x)} = \frac{1}{cos(x)}

    So when is cos(x) = 0? When
    x = \frac{\pi}{2} + 2\pi k = (4 k + 1)\frac{\pi}{2}
    and
    x = \frac{3\pi}{2} + 2\pi k = (4 k + 3)\frac{\pi}{2}
    where k is some integer. (I presume there is a typo in the x = b equation.)

    -Dan
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  3. #3
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    Well...
    I gave the wrong answer. That is the answer for the asymptotes. That cuased confusion I apologize for that.

    The actual answer is:
    lim as x--> a- f(x)= infinity
    lim as x--> a+ f(X)= - infinity

    lim as x--> b- f(x)= - infinity
    lim as x--> b+ f(X)= infinity


    The question was taken direct from the book so I can't help you with that.

    As for finding the asymptotes,
    I did indeed make a typo. You're answer is correct.

    I think I understand how you got to the asymptotes. You used the equation of a sinusoid without the cos in it. Cos (pi/2)= 0. And the 2pi/1 =2pi. k is some integer, or x in my book.
    Put it together and you have the asymptote for everything that starts on the top two quadrants.

    The other equation is just another of writing it.
    Yes? No?


    Thanks again!
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