Questions about proving \lim_{x \to 0} \frac{\sin x}{x}=1



Answered question


Questions about proving limx0sinxx=1

Answer & Explanation

Debbie Moore

Debbie Moore

Beginner2022-01-17Added 43 answers

A general result: let f(x)=n=0anxn be a power series with radius of convergence R>0, where R= is allowed.
If 0<r<R, then the power series converges uniformly on [−r,r]. Since the functions anxn are continuous, f is continuous on [−r,r]. Since r with 0<r<R was arbitrary, f is continuos on (−R,R).
In your example the sequence (fn) does not converge uniformly.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?