AP EAMCET2014MathematicsLimits
_ x 0 1+x^2 - 1-x+x^2 3^x-1 is equal to
Options
- A1 _e 3
- B_e 9
- C1 _e 9
- 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