Let $$f : (-\infty, \infty) - \{0\} \rightarrow \mathbb{R}$$ be a differentiable function such that $$f'(1) = \lim_{a \to \infty} a^2 f\left(\frac{1}{a}\right)$$. Then $$\lim_{a \to \infty} \frac{a(a+1)}{2} \tan^{-1}\left(\frac{1}{a}\right) + a^2 - 2\log_e a$$ is equal to

A

$$\frac{3}{2} + \frac{\pi}{4}$$

B

$$\frac{3}{4} + \frac{\pi}{8}$$

C

$$\frac{3}{8} + \frac{\pi}{4}$$

D

$$\frac{5}{2} + \frac{\pi}{8}$$