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anonymous

  • one year ago

how do you find the horizontal asymptote of f(x) = (4sin(x) )/(x^2 +1)

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  1. jim_thompson5910
    • one year ago
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    I would look at a table of values. Look at what happens to y as x gets bigger and bigger

  2. jim_thompson5910
    • one year ago
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    so plug in x = 10, x = 100, x = 1000, etc etc

  3. anonymous
    • one year ago
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    find the limit as x -> infinity, -infinity

  4. anonymous
    • one year ago
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    hint: sin x is bound between -1 and 1

  5. anonymous
    • one year ago
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    Is there a way to find it analytically?

  6. jim_thompson5910
    • one year ago
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    as pgpilot326 is saying, sine is bound from -1 to 1 ie, the smallest sin(x) can get is -1. The largest it can get is +1

  7. jim_thompson5910
    • one year ago
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    so 4sin(x) is completely bounded but x^2+1 can grow as big as it wants

  8. anonymous
    • one year ago
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    thanks :)

  9. jim_thompson5910
    • one year ago
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    no problem

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