Math - horizontal asymptote of f(x) (check)

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What is the horizontal asymptote of f(x)=x/(x-1)^2

It is supposed to be y=0 but then I even know that b/d is the horizontal asymptote, in this since there is no b, it would be 0/1 which is 0

is the above reasoning correct?

  • Math - horizontal asymptote of f(x) (check) -

    horizontal asymptote occurs where the value of x is restricted,,
    n the given function f(x)=x/(x-1)^2, what value of x is restricted?

  • Math - horizontal asymptote of f(x) (check) -

    oops i got it wrong
    horizontal asymptote occurs where the value of y is restricted,,
    so in the given function f(x)= y = x/(x-1)^2, what value of y is restricted?

  • Math - horizontal asymptote of f(x) (check) -

    your function expanded is

    f(x) = x/(x^2 - 2x + 1)

    For a horizontal asymptote we look at what happens to the function as x ---> infinity.

    Use an intuitive approach ...
    as x becomes very large, say x = 1 million, the denominator becomes large much faster than the numerator.
    So you have a division by a hugely large number resulting in a number close to zero
    So when x ---> + infinity, f(x) ---> +0 (still above the x-axis)
    wen x ---> - infinity , f(x) ----> -0 (slightly below the x-axis)

  • Math - horizontal asymptote of f(x) (check) -

    is it that the y-value is restricted to being positive. sine the horizontal asymptote has an equation of y=0.

  • Math - horizontal asymptote of f(x) (check) -

    horizontal asymptote:
    y = 0 , as x approaches plus/minus infinity

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