AP EAMCET20226 Jul 2022Evening ShiftMathematicsLimitsActual

_ x 0 ( e^x-1 x )^ x x+1-e^x =

Options

Ae
Be⁻¹
Ce^2
De⁻²

Correct answer

B. e⁻¹

Step-by-step solution

aligned & _ x 0 ( e^x-1 x )^ x x+1-e^x = & _ x 0 [1+ e^x-1 x -1 ]^ x x+1-e^x = & _ x 0 [1+ e^x-1-x x ]^ -x e^x-1-x = & e⁻¹ [ _ x 0 (1+x)^ 1 x =e ] aligned

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