If x is a real number in [0, 1] then the value of _ m _ n [1 + cos 2m (n!πx)] is given…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
If x is a real number in [0, 1] then the value of
\(\lim _{m \rightarrow \infty} \lim _{n \rightarrow \infty}\)[1 + cos2m(n!πx)] is given by, where [x] represents greatest integer < x.
\(\lim _{m \rightarrow \infty} \lim _{n \rightarrow \infty}\)[1 + cos2m(n!πx)] is given by, where [x] represents greatest integer < x.
- 2 if x is rational
- 1 for all x
- 1 if x is irrational
- 2 for all x
Answer
(A) 2 if x is rational, (C) 1 if x is irrational
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