![real analysis - Continuity of the function $f(x)=\lim\limits_{n \to \infty}[\lim\limits_{t\to 0}[\frac{\sin^2 (n!\pi x)}{\sin^2(n! \pi x)+t^2}]] $, $x \in \mathbb R$ - Mathematics Stack Exchange real analysis - Continuity of the function $f(x)=\lim\limits_{n \to \infty}[\lim\limits_{t\to 0}[\frac{\sin^2 (n!\pi x)}{\sin^2(n! \pi x)+t^2}]] $, $x \in \mathbb R$ - Mathematics Stack Exchange](https://i.stack.imgur.com/8ziM5.jpg)
real analysis - Continuity of the function $f(x)=\lim\limits_{n \to \infty}[\lim\limits_{t\to 0}[\frac{\sin^2 (n!\pi x)}{\sin^2(n! \pi x)+t^2}]] $, $x \in \mathbb R$ - Mathematics Stack Exchange
![Limit (1+1/n)^n = e as n approaches to infinity (W/Text Explanation) Proof | Maths |Mad Teacher - YouTube Limit (1+1/n)^n = e as n approaches to infinity (W/Text Explanation) Proof | Maths |Mad Teacher - YouTube](https://i.ytimg.com/vi/3Wb0jPhuRco/hqdefault.jpg)
Limit (1+1/n)^n = e as n approaches to infinity (W/Text Explanation) Proof | Maths |Mad Teacher - YouTube
![lim)┬(n→∞)〖(sin π/2n.sin 2π/2n.sin 3π/2n…….sin ((n-1)π)/2n)^(1/n) 〗 is equal to: a)1/2 b) 1/3 - YouTube lim)┬(n→∞)〖(sin π/2n.sin 2π/2n.sin 3π/2n…….sin ((n-1)π)/2n)^(1/n) 〗 is equal to: a)1/2 b) 1/3 - YouTube](https://i.ytimg.com/vi/OUE0svgrp68/maxresdefault.jpg)