Set, Relation and FunctionHard
Question
For every integer n, let an and bn be real numbers. Let function f : IR → IR be given by f(x) = 
, for all integers n. If f is continuous, then which of the following hold(s) for all n?
, for all integers n. If f is continuous, then which of the following hold(s) for all n?Options
A.an-1-bn-1 = 0
B.an-bn = 1
C.an -bn+1 = 1
D.an-1 -bn = - 1
Solution
At x = 2n
L.H.L. =
(bn + cos π (2n - h)) = bn + 1
R.H.L. = (an + sin π (2n + h)) = an
f(2n) = an
For continuity bn + 1 = an
At x = 2n + 1
L.H.L = (an + sin π (2n + 1 - h)) = an
R.H.L = (bn+1 + cos (π (2n + 1 - h))) = bn+1 - 1
f(2n + 1) = an
For continuity
an = bn+1 - 1
an-1 - bn = - 1.
L.H.L. =
(bn + cos π (2n - h)) = bn + 1R.H.L. =
(an + sin π (2n + h)) = anf(2n) = an
For continuity bn + 1 = an
At x = 2n + 1
L.H.L =
(an + sin π (2n + 1 - h)) = anR.H.L =
(bn+1 + cos (π (2n + 1 - h))) = bn+1 - 1f(2n + 1) = an
For continuity
an = bn+1 - 1
an-1 - bn = - 1.
Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
A ship is fitted with three engines E1, E2 and E3. The engines function independently of each other with respective prob...Let f:R → , where f(x) = tan-1 , then-...Let f, g and h be real-valued functions defined on the interval [0, 1] by f(x) = ex2 + e- x2, g(x)= xex2 + e- x2 and h (...Let A = {2, 3, 4, 5} and let R = {(2, 2), (3, 3), (4, 4), (5, 5), (2, 3), (3, 2), (3, 5), (5, 3)} be a relation in A. Th...Let a relation ′R′ is define on ′Z′ set of integers such that a R b ⇒ a is divisible by b ...