I'm looking for an exercise's book with valid examples of how to solve limitis of summations and limits of definite integrals. Here some examples:
$\lim_{a\to 0} a\int_{-a}^a\frac{cos x}{x^2 + a^2}$
$\lim_{n\to\infty} \frac{1}{ln n} \sum_{k=0}^{n-1} \frac 1k$
$\lim_{n\to\infty} n^2 \sum_{k=0}^{n-1} sin (2\pi\frac kn)$
Thank you!