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anonymous

  • 5 years ago

find the oblique asymptotes of f(x) = (9x-x^3)/(x^2-4). Is this oblique asymptote a linear or nonlinear asymptote

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  1. amistre64
    • 5 years ago
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    the bottom and top exponent differ by only one degree which means that this oblique is linear....

  2. amistre64
    • 5 years ago
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    better put... that highest exponents on top and bottom only differ by one degree; so the oblique is a line

  3. anonymous
    • 5 years ago
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    Can you explain how I could solve the equation

  4. amistre64
    • 5 years ago
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    solve it for the oblique you mean?

  5. anonymous
    • 5 years ago
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    yes

  6. amistre64
    • 5 years ago
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    long division: -x ------------ x^2 -4 |-x^3 +9x x^3 -4 --------- 9x -4 <- remainder the oblique takes the shape of: 9x-4 -x + ------ x^2-4 the left side part goes to zero is x gets large which means that y = -x+0 or simply y = -x is the equation of the line for your oblique asymptote

  7. amistre64
    • 5 years ago
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    and by left side I mean right side.... Oy!!

  8. anonymous
    • 5 years ago
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    Ok, let me study this for a second. thanks

  9. amistre64
    • 5 years ago
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    your seconds up :)

  10. amistre64
    • 5 years ago
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    as the bottom of a fraction gets very large: 1 ----------------------------- 1000000000000000000000000 the value of the fraction get very very very tiny and gets close to zero at the ends.

  11. amistre64
    • 5 years ago
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    so anything with an "x" in the bottom gets thrown out and counted for zero

  12. anonymous
    • 5 years ago
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    y = -x+0 would mark the end of the equation?

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