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BITSAT2010MathematicsContinuity and DifferentiabilityActual

Let (f(x)= (e^x-1 )^2 ( x a ) (1+ x 4 ) ) for (x 0 ), and (f(0)=12 ). If ( f ) is continuous at (x=0 ), then the value of (a ) is equal to

Options

  1. A1
  2. B-1
  3. C2
  4. D3

Correct answer

D. 3

Step-by-step solution

( aligned & Lt _ x 0 (e^x-1 )^2 ( x a ) (1+ x 4 ) &= Lt _ x 0 (e^x-1 )^2 x x^2 x a ( x a ) ( x a ) (1+ x 4 ) x 4 x 4 4 a=12 & a=3 aligned )

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