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Limits Continuity and Differentiability question

2012 · Shift 2 · Q38
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  2. /JEE Advanced
  3. /Mathematics
  4. /Limits Continuity and Differentiability
  5. /2012 · Shift 2 · Q38

Limits Continuity and Differentiability question

2012 · Shift 2 · Q38

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −1
For every integer n, let an and bn be real numbers. Let function f : R →\to→ R be given by f(x)={an+sin⁡πx,for x∈[2n,2n+1]bn+cos⁡πx,for x∈(2n−1,2n)f(x) = \left\{ {\begin{matrix} {{a_n} + \sin \pi x,} & {for\,x \in [2n,2n + 1]} \\ {{b_n} + \cos \pi x,} & {for\,x \in (2n - 1,2n)} \\ \end{matrix} } \right.f(x)={an​+sinπx,bn​+cosπx,​forx∈[2n,2n+1]forx∈(2n−1,2n)​, for all integers n. If f is continuous, then which of the following hold(s) for all n ?
  1. A
    an −-− 1 −-− bn −-− 1 = 0
  2. B
    an −-− bn = 1
  3. C
    an −-− bn +++ 1 = 1
  4. D
    an −-− 1 −-− bn =−-− 1
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