AP EAMCET202422 May 2024Morning ShiftMathematicsLimitsActual
If f(x)= ( 1+x 1-x )^ 1 x is continuous at x=0 then f(0)=
Options
- Ae^ 1 2
- Be^2
- Ce⁻²
- De^ -1 2
Correct answer
B. e^2
Step-by-step solution
f(x)= ( 1+x 1-x )^ 1 x is continuous at x=0 f(0)= _ x 0 f(x) Now, _ x 0 f(x)= _ x 0 ( 1+x 1-x )^ 1 x ( 1^ form) aligned & =e^ _ x 0 1 x ( 1+x 1-x -1 ) =e^ _ x 0 1 x ( 1+x-1+x 1-x ) & =e^ _ x 0 ( 2 1-x ) =e^2 f(0)=e^2 . aligned