Lim as x goes to infinity cosx?

Question

lime as x goes to infinity sin x?

They both don't exist right? because it oscillates too much?

Answer 1

Right.

Answer 2

Yes, you're right. But why?
What does it mean for a function to go to a limit as x goes to infinity? It means there's a single number L such that no matter how close I specify, the function not only gets that close, but stays that close. So you can visualize it as a narrowing triangle with L the axis and as x goes to infinity, f(x) remains in that triangle. Now you can see that sinx and cosx can't have a limit because there's no narrowing triangle that would contain them,
Notice the difference with something like sinx/x . Although the sinx contiues to cycle up and down, the x in the denominator is drawing the amplitudes down into a decreasing triangle.

Answer 3

Hey there!

The limit does not exist, since the graph fluctuates up and down in the interval -pi/2≤x≤pi/2. Since the graph does not remain constant, the limit does not exist.

Hope it helps!

Answer 4

Correct, neither limit exists.