infinite limitation

Question

lim sin( π /x)/(πx)

x→∞ 

Answer 1

Well as x > ∞, (π/x) > 0, so sin (π/x) > 0, and πx > ∞, so the limit will go to 0/∞ = 0.

You can check this by graphing the function (make sure you are working in radians) and using the trace function to see what happens to f(x) when x gets larger and larger

Mike