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

1 Answer
NickTheTurtle
Jul 25, 2018

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.

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