Question

How do you find `lim sintheta` as `theta->oo`?

Answer 1

Does not exist

Explanation:

`sin(theta)` oscillates in between `-1` and `1` as `theta` approaches `oo`. In other words, it does not converge to a single value.

One way to show this is through the definition of a limit to positive infinity, which states that, if `lim_(x->oo)f(x)=L`, then for any given `epsilon>0`, however small, there exists some `c` such that `L-epsilon<= f(x)<= L+epsilon` for all `x>c`.

This is clearly impossible for `lim_(theta->oo)sin(theta)`, as no matter how large `theta` is, `sin(theta)` will still oscillate between `-1` and `1`. Thus, the limit does not exist.