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If f x = 1 + 5 + x - a x - 4 0 ≤ x < 4 b x ≥ 4 is continuous at x = 4 , then value of 1 a b is equal to

Correct answer

12

Step-by-step solution

∵ f x is continuous at x = 4 ∴ l i m x → 4 - f x = l i m x → 4 + f x = f 4 l i m x → 4 - 1 + 5 + x - a x - 4 = b for numerator to be zero ⇒ a = 2 now after rationalization, l i m x → 4 - 1 + 5 + x - 2 1 + 5 + x + 2 x - 4 1 + 5 + x + 2 = b l i m x → 4 - 1 + 5 + x - 4 x - 4 4 = b again on rationalization, l i m x → 4 - 5 + x - 9 x - 4 × 4 5 + x + 3 = b 1 4 × 6 = b ⇒ b = 1 24 1 a b = 24 2 = 12

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