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BITSAT2014MathematicsContinuity and DifferentiabilityActual

Let f ( x )= array l 1- ³ x 3 ² x , x 2 array . If f(x) is continuous at x= 2 ,(p, q)=

Options

  1. A(1,4)
  2. B( 1 2 , 2 )
  3. C( 1 2 , 4 )
  4. DNone of these

Correct answer

C. ( 1 2 , 4 )

Step-by-step solution

f [( / 2)⁻ ]= _ h 0 1- ³[( / 2)- h ] 3 ²[( / 2)- h ] = _ h 0 1- ³ ~h 3 ² ~h = 1 2 f [( / 2)⁺ ]= _ h 0 q [1- ( / 2)+ h ] [ -2 ( / 2)+ h ]² = _ h 0 q (1- ) 4 ~h ² = q 8 p = 1 2 = q 8 p = 1 2 , q =4

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