What is the limit of sin (1/x)? - Week 1 - Lecture 8 - Mooculus

[tomoaks]

her's a much easier explanation: 1/x could be either an odd or an even multiple of pi. That means that close to 0, sin(1/x) could be 1 or -1, or any number in-between.

[gideonspaulding]

Budding mathematician and current math teacher. Love your videos!

[SumaidSyed]

Great Explanation!! But is there any mathematical way to prove that lim of sin1/x does not exist?I mean do we always need to use graphs/values to prove that?

[Supware]

Awesome! Super interesting problem very well explained

[北村明-jn]

The true representation of real numbers (forced numbers) must be accompanied by an operator such as "/" or "sin". But the answer can only be expressed in rational numbers. Like "1/3 = 0.333 ...". That's a misunderstanding. All answers can only be written as rational numbers.

[muhammadarafat]

Thank you for making this free.

I have a question regarding the limit of sin(1/x) as x approaches 0. Looking back at the graph, well, it's certainly not clear what f(x) is approaching as x approaches 0, but in the end, sin(g(x)) is a periodic function, and it has some period that it oscillates back and forth about, it's just that the period gets infinitely small as x approaches 0. Getting back to the question, what I want to ask is the following: How small can we make x to 0 in order to say that it has a limit? it's clearly approaching something for infinitely small change, yet we tell that the limit does not exist because we cannot detect the value it's approaching.

[arpitamukherjee]

the graph & ur hair are same in style😅