If the function f x = x + a 2 sin x 0 ≤ x π 4 2 x cot x + b π 4 ≤ x ≤ π 2 a cos 2 x - b sin x π 2 x ≤ π is continuous in 0 , π , then the values of a and b respectively are

Question

If the function f x = x + a 2 sin x 0 ≤ x π 4 2 x cot x + b π 4 ≤ x ≤ π 2 a cos 2 x - b sin x π 2 x ≤ π is continuous in 0 , π , then the values of a and b respectively are, π 6 , - π 12, - π 6 , π 4, - π 3 , π 12, None of these

MARKS App · Accepted Answer

∵ f x is continuous in 0 , π so it is continuous at x = π 4 and x = π 2 ∴ lim x → π 4 - f x = lim x → π 4 + f x ⇒ π 4 + a = π 2 + b .....(1) and lim x → π 2 - f x = lim x → π 2 + f x ⇒ 0 + b = - a - b .....(2) By solving (1) and (2), we get, a = π 6 , b = - π 12

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