Any $\varepsilon$-$\delta$ proof of this limit statement using only the trigonometric or circular definition of the sine function?
34127
Prove $\lim_{x \rightarrow 0} \frac {\sin(x)}{x} = 1$ with the epsilon-delta definition of limit.
151329
Showing $\lim_{(x,y) \to (0,0)} \sin (xy) / xy = 1$
68830
How to prove that $\lim\limits_{\epsilon\rightarrow 0}\int_{-\infty}^{\infty}f_\epsilon(x)g(x)dx=g(0)$ (Dirac delta function))
53213
How to prove that $\lim(\underset{k\rightarrow\infty}{\lim}(\cos(|n!\pi x|)^{2k}))=\chi_\mathbb{Q}$
64628
Solving limits of a sine wave $\lim_{x\to+\infty}\frac{\sin(x)}{x}$
133874
Proof that $\lim_{n\to\infty}{\sin{100n}}$ does not exist
150917
Show that $\lim_{n\to \infty}\sin{n\pi x} =0$ if $x\in \mathbb{Z},$ but the limit fails to exist if $x\notin \mathbb{Z}.$
150308
How to prove that $\lim\limits_{n\to\infty}\int\limits _{a}^{b}\sin\left(nt\right)f\left(t\right)dt=0\text { ? }$
131140
Understanding ProofWiki's proof of differentiation of sine power series
78941
proof that an alternative definition of limit is equivalent to the usual one
141260
Prove using the formal definition of a limit that
135565
Limit of $\frac{1}{x^2}-\frac{1}{\sin^2(x)}$ as $x$ approaches $0$
112481
Given $a_{n+1} = \frac{{a_n}}{\sin({a_n})}$ with $0 < a_1 < \frac{\pi}{2}$. Show that the limit $\lim_{n\rightarrow\infty}{a_n}$ exists and find it.
85388
Prove that the limit of $\sin n$ as $n \rightarrow \infty$ does not exist
150601
The limit of $\sin(1/x)$ as $x\to 0$ does not exists
85412
Epsilon delta proof for $\lim_\limits{x\to a} \sqrt{x} = \sqrt{a}$ where $a>0$
47606
Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit