Let f:(-∞, ∞)-{0} → R be a differentiable function such that f^′(1)= lim_a → ∞ a^2 f(1/a). Then lim_a → ∞ (a(a+1))/2 tan^-1(1/a)+a^2-2 log_e a is…

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