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AP EAMCET202316 May 2023Evening ShiftMathematicsContinuity and DifferentiabilityActual

If a function defined by f(x)= (3^x-1 )^2 x (1+x) , x 0 , is continuous at x =0 , then f (0)=

Options

  1. A2 3
  2. B3^2
  3. C2+ 3
  4. D( 3)^2

Correct answer

B. 3^2

Step-by-step solution

Given f(x)= (3^x-1 )^2 x (1+x) , x 0 Now, _ x 0 f(x)= _ x 0 (3^x-1 )^2 x (1+x) aligned & = _ x 0 ( 3^x-1 x )^2 x x (1+x) x & = ( 3)^2 1 1 =( 3)^2 aligned Since f(x) is continuous at x=0 So _ x 0 f(x)=f(0) f(0)=( 3)^2

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