For every integer n , let a_ n and b_ n be real numbers. Let function f: I R I R be given by f(x)= array lll a_ n + x, & for & x [2 n, 2 n+1] b_ n + x, & for & x (2 n-1,2 n) array . for all integers n . If f is continuous, then which of the

Question

For every integer n , let a_ n and b_ n be real numbers. Let function f: I R I R be given by f(x)= array lll a_ n + x, & for & x [2 n, 2 n+1] b_ n + x, & for & x (2 n-1,2 n) array . for all integers n . If f is continuous, then which of the following hold (s) for all n ?

Quantrex Academy · Accepted Answer

Correct answer: B. a_ n -b_ n =1

Given : f(x)= array ll a_ n + x, & x [2 n, 2 n+1] b_ n + x, & x (2 n-1,2 n) array . f is continuous for all n At x=2 n, LHL = RHL =f(2 n) b_ n + 2 n=a_ n + 2 n=a_ n + 2 n b_ n +1=a_ n a_ n -b_ n =1, option (b) is correct. Also at x=2 n+1, LHL = RHL =f(2 n+1) _ h 0 a_ n + (2 n+1-h)= _ h 0 b_ n+1 + (2 n+1-h)=a_ n + (2 n+1) a_ n =b_ n+1 -1=a_ n a_ n -b_ n+1 =-1 option (c) is incorrect. a_ n-1 -b_ n =-1, option (d) is correct.

For every integer n , let a_ n and b_ n be real numbers. Let function f: I R I R be given by f(x)= array lll a_ n + x, & for & x [2 n, 2 n+1] b_ n + x, & for & x (2 n-1,2 n) array . for all integers n . If f is continuous, then which of the following hold (s) for all n ?

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