For every integer n , let a n and b n be real numbers. Let function f : R → R be given by…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
For every integer n, let an and bn be real numbers.
Let function f : R→ R be given by
\(f(x)=\left\{\begin{array}{l} a_{n}+\sin \pi x, \text { for } x \in[2 n, 2 n+1] \\ b_{n}+\cos \pi x, \text { for } x \in(2 n-1,2 n) \end{array}\right.\)
for all integers n. If f is continuous, then which of the following hold(s) for all n?
Let function f : R
\(f(x)=\left\{\begin{array}{l} a_{n}+\sin \pi x, \text { for } x \in[2 n, 2 n+1] \\ b_{n}+\cos \pi x, \text { for } x \in(2 n-1,2 n) \end{array}\right.\)
for all integers n. If f is continuous, then which of the following hold(s) for all n?
- an–1 – bn–1 = 0
- an – bn = 1
- an – bn+1 = 1
- an–1 – bn = –1
Answer
(B) a n – b n = 1
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