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

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I would look at a table of values. Look at what happens to y as x gets bigger and bigger

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so plug in x = 10, x = 100, x = 1000, etc etc

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0find the limit as x > infinity, infinity

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hint: sin x is bound between 1 and 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is there a way to find it analytically?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1as 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

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so 4sin(x) is completely bounded but x^2+1 can grow as big as it wants
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