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For every integer n, let an and bn be re...

For every integer n, let `a_n` and `b_n` be real numbers Let function `f : R rarr R` be given by
`f(x)={(a_n+ sin pi x, "for" x in [2n, 2n+1]), (b_n+cos pi x, "for" x in (2n-1,2n)):}`
for all integers n If f is continuous, then which of the following hold(s) for all n ?

A

`a_(n-1) - b_(n-1) = 0`

B

`a_n - b_n = 1`

C

`a_n - b_(n+1) = 1`

D

`a_(n-1) - b_n = 1`

Text Solution

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The correct Answer is:
B, D
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