Thursday, March 7, 2019

real analysis - How to use formal limit definition?

(a) IF lim THEN \lim _{x \rightarrow \infty} \sin (f(x)) does not exist.



I know that this statement is false.




I will give a counterexample for this as just take f(x) = \lfloor x \rfloor \pi.
How to prove that using formal definition of limit that this example violate above statement.

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