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AP EAMCET202120 Aug 2021Morning ShiftMathematicsContinuity and DifferentiabilityActual

If the function f ( x ) , defined below, is continuous on the interval [ 0 , 8 ] , then f ( x ) = x 2 + a x + b , 0 ≤ x < 2 3 x + 2 , 2 ≤ x ≤ 4 2 a x + 5 b , 4 < x ≤ 8

Options

  1. Aa = 3 ,   b = - 2
  2. Ba = - 3 ,   b = 2
  3. Ca = - 3 ,   b = - 2
  4. Da = 3 ,   b = 2

Correct answer

A. a = 3 ,   b = - 2

Step-by-step solution

Given that f ( x ) = x 2 + a x + b , 0 ≤ x < 2 3 x + 2 , 2 ≤ x ≤ 4 2 a x + 5 b , 4 < x ≤ 8 Since f ( x ) is continuous on 0 , 8 i.e. f x is continuous at x = 2 and x = 4 L . H . L = f ( x ) = R . H . L lim x → 2 f x = f ( 2 ) lim x → 2 x 2 + a x + b = 3 x + 2 = 8 4 + 2 a + b = 6 + 2 o r   2 a + b = 4         ( i ) . . . . f ( 4 ) = lim f ( x ) x → 4 3 x + 4 = 3 4 + 2 = lim x → 4 2 a x + 5 b   14 = 8 a + 5 b       &#

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