Let f be continuously differentiable 2 π periodic real valued function on the real line. Let \(a_n = \int_{-\pi}^{\pi} f(t) cos (nt) dt\) where n is non negative integer then choose the correct option?
1
The derivative of f is also a 2π - periodic function
2
The derivative of f is not a 2π - periodic function
3
\(|a_n|\le C \frac{1}{n}\) for all n, where C > 0 is a constant independent of n.
4
an → 1 as n → ∞