AP EAMCET202316 May 2023Morning ShiftMathematicsLimitsActual
_ n 1 n ( 1 e^ 1 / n + 1 e^ 2 / n + 1 e^ 3 / n + + 1 e^2 )=
Options
- A1- e ⁻²
- B1+ e ⁻²
- Ce ^2-1
- De ^2+1
Correct answer
A. 1- e ⁻²
Step-by-step solution
_ h 1 n ( 1 e^ 1 / n + 1 e^ 2 / n + 1 e^ 3 / n + .+ 1 e^2 )= _ h 1 n _ k=1 ^ 2 n 1 e^ k / n aligned & = ₀^2 1 e^x d x= ₀^2 e^ -x d x= [-e^ -x ]₀^2 & =-e⁻²+e^0=1-e⁻² aligned