For every integer n, let a_n and b_n be real numbers. Let function f : R → R be given by f (x) = \{\table a_n + \sin\pix , \for \x ∊ [2n,2n+1];b_n + \cos\pix , \for \x ∊ (2n-1,2n), for all integers n. If f is continuous, then which of the following hold(s) for all n? [JEE Adv 2012 P2]

Limits, Continuity and Differentiability

Section: Mathematics

Question : 41 of 51

Marks: +1, -0

For every integer n, let an and bn be real numbers. Let function
f : R → R be given by
f (x) =

{

an+sinπx	for‌x∊[2n,2n+1]
bn+cosπx	for‌x∊(2n−1,2n)

, for all integers n. If f is continuous, then which of the following hold(s) for all n?

[JEE Adv 2012 P2]

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