Proving $f(x) = \frac{\sin x}{x}$ converges by improper integral test?
83966
Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral?
141218
Does $\sum_{n=1}^{\infty} \frac{\sin(n)}{n}$ converge conditionally?
122301
Evaluating and proving $\lim\limits_{x\to\infty}\frac{\sin x}x$
45517
Prove Taylor series converges to $f$.
133333
Find $f(x)$ for $f(f(x))=\sin x$
25503
Convergence of $\sum_{n=1}^\infty \frac{\sin^2(n)}{n}$
21240
Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only
107351
Evaluate the improper integral $\int_{0}^{\infty}{f(x)-f(2x)\over x}dx$, where $\lim_{x \to \infty} f(x) = L$
51837
Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$
87242
Ways to prove $ \int_0^\pi dx \frac{\sin^2(n x)}{\sin^2 x} = n\pi$
83064
Is the Series Sin(k)/k Absolutely Convergent?
157762
Showing $f_n(x):=\frac{x}{1+n^2x^2}$ uniformly convergent in $\mathbb R$ using $\epsilon-n_0$
129078
Proving the series $\sum_{n=0}^{\infty}\sin(e\pi n!)$ converges
129823
Show that $\sum_{n=1}^{\infty}(n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+\frac{1}{6})$ converges
53885
$\forall a > 0$ $\sum_{n=1}^{\infty} f(na)$ is convergent. Prove that $\int_{0}^{\infty}f(x) dx$ is convergent.
61696
Prove that $\{x_1=1,\,x_{n+1}=\frac {x_n}2+\frac 1{x_n} \}$ converges when $n \to \infty$
69348
Prove that $\int \limits _{0}^{\infty}\frac{e^{-2x}-e^{-ax}}{x}\text{d}x$ converges for any $a>0$