If _ x 0⁺ x^2 ( e^ 1 / x -e^ -1 / x e^ 1 / x +e^ -1 / x )=k and _ x 0⁻ x^2 ( e^ 1 / x -e^ -1 / x e^ 1 / x +e^ -1 / x )=l , then

Step-by-step solution

k= _ x 0⁺ x^2 [ e^ 1 x -e^ -1 x e^ 1 x +e^ -1 x ] Let 1 x =tx 0⁺, t = _ t 1 t^2 [ e^t-e^ -t e^t+e^ -t ]= _ x 1 t^2 [ 1-e^ -2 t 1+e^ -2 t ]=0 [ array l _ t 1 e^ 2 t =0 and _ t 1 t^2 =0 array ]l= _ x 0⁻ x^2 [ e^ 1 x -e^ - 1 x e^ 1 x +e^ - 1 x ] Let 1 x =yx 0⁻, y - l= y 1 y^2 [ e^y-e^ -y e^y+e^ -y ]=0 [same as above] k=l