Here's a proof by the squeeze theorem.. Consider a unit circle as in the diagram below. The right-angled triangle ABC has hypotenuse 1

Reference: How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? I think that all proofs above are beautiful but I cannot see why we have to complicate it.

2016年1月2日 · $\begingroup$ @Wojowu Can you explain or give an example of what you mean by your last sentence? This might be a simplification of Simple Art's question, but I think he was essentially asking for a way to evaluate $\sin(x) = x$ using only the techniques at the disposal of someone in early high school i.e. someone who hadn't learned calculus or analysis yet.

EVALUTING THE LIMIT $\displaystyle \lim_{x\to 0}\frac{\sin(x)}{x}$ Using standard analysis (e.g. L'Hospital's rule), and without appeal to any a priori knowledge of properties of $\sin (x)$ and $\cos (x)$, one can derive easily the limit sought.

2017年6月14日 · I was having trouble with the following integral: $\int_{0}^\infty \frac{\sin(x)}{x}dx$. My question is, how does one go about evaluating this, since its existence seems fairly intuitive, while its

But then, you also learn that smart Mathematicians have managed to find a solution by introducing the concept of limit: lim(x-->0){sinx/x}=1. You take your hat off fo the genius of Math, to make sure you compute the limit from the left and the limit from the right and find them equal 1 and so, now, you may think that you can plot the continuous ...

Improper integral of $\sin(x)/x $ converges absolutely, conditionally or diverges?. We have $$\int_1^{\infty}\frac{\sin x}{x}\text{d}x$$

2014年6月16日 · I'm looking for a really basic proof of $\sin(-x) = -\sin(x)$. The proof should pretty much only employ basic trigonometry.

2015年5月8日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2015年12月27日 · I'm trying to find a proof that: $$ \lim_{x\to0^-}\sin(x)=0$$ I'd like to be able to do the proof without reference to advanced theorems (mean value theorem, series, etc).