Find the limit by expressing it as a definite integral of an appropiate function via Riemann Sums.
30063
How do you calculate this limit $\lim_{n\to\infty}\sum_{k=1}^{n} \frac{k}{n^2+k^2}$?
78444
Limit of definite integral of $f(x)\cos(mx)$
45728
Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$
67953
Finding the asymptotic of an integral
119469
Find the limit of $\lim\limits_{(x,y)\to (0,0)} \frac{x^2y^2}{x^2y^2+(x-y)^2}$
123568
Solving limit given a limit
4643
The limit of truncated sums of harmonic series, $\lim\limits_{k\to\infty}\sum_{n=k+1}^{2k}{\frac{1}{n}}$
17438
Evaluate $\lim_{n\to \infty} \sum_{r=1}^n \frac {1}{2^r}\tan \left(\frac {1}{2^r}\right)$
1057
How prove this integral limit $=f(\frac{1}{2})$
150971
If $f$ is Riemann integrable on $[0,1]$ then $\lim\limits_{n\rightarrow\infty}\frac{1}{n}\sum f\left(\frac{k}{n}\right)=\int\limits_{0}^{1} f(x)dx$
131739
Is my proof of the additivity property of Riemann integral correct?
17872
Evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}}$
20089
Prove that $\lim_{N\rightarrow\infty}(1/N)\sum_{n=1}^N f(nx)=\int_{0}^1f(t)dt$
56867
Convergence proof that involves integral
126256
Prove limit of function
157972
Find a closed form expression for $\sum\limits_{i=0}^{\infty} i^2\cdot x^i$
49860
Determine the convergence of $\sum\limits_{n=2}^\infty \frac{\sqrt{n+1}}{n(n-1)}$