calc

find the horizontal asymptotes of the curve....? im not sure what to do? thanks



y=14x/(x^4+1)^(1/4)

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asked by adam
  1. use some intuition here.

    we get horizontal asymptotes as we consider what happens when x ---> infinity

    look at the denominator of (x^4 + 1)^(1/4)

    as x gets larger, say x = 1000, adding 1 to x^4 won't make one hoot of difference, so in effect we are taking the fourth root of x^4, which is x
    so as x gets bigger, the denominator approaches x itself
    so we have approximately y =14x/x or
    y = 14 , if x becomes +large

    when x approaches infinity to the left, the numerator is negative, but the denominator stays positive, so we have
    y = -14

    notice the graph crosses at (0,0) and rises to y = 14 on the right, and drops to y = -14 on the left.

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    posted by Reiny

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