- #1
Ryker
- 1,086
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Homework Statement
What is the limit of sinx as x approaches π/3? Prove it.
The Attempt at a Solution
I was wondering, can one approach this using that theorem that reduces the properties of limits of functions to the properties of limits of sequences? Or does that lead to circular logic, because you're saying if xn tends to π/3, then f(xn) = tends to sin(π/3) = √3/2, but you haven't actually proven that the sequence that is a sine of another sequence converging to certain number actually converges to the sine of that number.
I was also playing around with trying to prove that the delta-epsilon way, but I haven't gotten anywhere.
So does anyone know how to prove this? Maybe I'm just overthinking this, and it's something really simple, but I guess that's why I'd appreciate your input.