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KCET2019MathematicsContinuity and Differentiability

If ( f(x)= array cc 3 x e^ 2 x -1 & x 0 k-2 & x=0 array . ) is continuous at ( x=0 ), then ( k= )

Options

  1. A( 9 5 )
  2. B( 2 3 )
  3. C( 3 2 )
  4. Dnone

Correct answer

D. none

Step-by-step solution

Given Options are not matching ( f(x)= array c 3 x e^ 2 x -1 x 0 k-2 x=0 array . ) Since ( f ) is continuous at ( x=0 ) ( lt _ x 0 f(x)=f(0) ) ( _ x 0 3 x 2 x-1 =k-2 ) ( _ x 0 3 x x e^ 2 x -1 x =k-2 ) ( _ x 0 3 x x lt e^ 2 x -1 x =k-2 ) ( 3 2 =k-2 k= 3 2 +2= 7 2 ) ( k= 7 2 ) ( lt _ x 0 f(x)=f(0) ) ( _ x 0 3 x 2 x-1 =k-2 ) ( _ x 0 3 x x e^ 2 x -1 x =k-2 ) ( _ x 0 3 x x lt _ x 0 e^ 2 x -1 x =k-2 ) ( 3 2 =k-2 k= 3 2 +2= 7 2 ) ( k = 7 2 )

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