COMEDK2024MathematicsLimits

The value of _ x 0 ( 2+x 2-x )^ 1 x is

Options

Ae
Be^2
Ce^-2
De^ -1 2

Correct answer

A. e

Step-by-step solution

Put x=0 aligned & ( 2+0 2-0 )^ 1 0 =1^ & e^ _ x 0 ( 2+x 2-x -1 ) 1 x &[ . _ x 0 [f(x)]^ g(x) =e^ _ x 0 g(x)[f(x)-1] ] & =e^ _ x 0 [ 2+x-2+x x(2-x) ] e^ _ x 0 2 2-x aligned Put x=0 , e^ 2 2 =e^1

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