Question

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

Answer 1

I would look at a table of values. Look at what happens to y as x gets bigger and bigger

Answer 2

so plug in x = 10, x = 100, x = 1000, etc etc

Answer 3

find the limit as x -> infinity, -infinity

Answer 4

hint: sin x is bound between -1 and 1

Answer 5

Is there a way to find it analytically?

Answer 6

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

Answer 7

so 4sin(x) is completely bounded but x^2+1 can grow as big as it wants

Answer 8

thanks :)

Answer 9

no problem