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AP EAMCET2014MathematicsLimits

_ x 0 1+x^2 - 1-x+x^2 3^x-1 is equal to

Options

  1. A1 _e 3
  2. B_e 9
  3. C1 _e 9
  4. D_e 3

Correct answer

C. 1 _e 9

Step-by-step solution

aligned & _ x 0 1+x^2 - 1-x+x^2 3^x-1 & = _ x 0 1+x^2 - 1-x+x^2 3^x-1 & 1+x^2 + 1-x+x^2 1+x^2 + 1-x+x^2 & = _ x 0 (1+x^2 )- (1-x+x^2 ) 3^x-1 ( 1-x^2 + 1-x+x^2 ) & = _ x 0 x (3^x-1 ) 1 ( 1-x^2 + 1-x+x^2 ) & = _ x 0 1 3^x-1 x 1 1-x^2 + 1-x+x^2 & = _e 1 3 1 1-0 + 1-0+0 & [ (a^x-1 ) x =1 ] & = 1 2 _e 3 = 1 _e 9 & aligned

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