If = x 0 Lt x 2^x-x 1- x and = Lt _ x 0 x 2^x-x 1+x^2 - 1-x^2 , then

Step-by-step solution

We have, aligned & = _ x 0 x 2^x-x 1- x & [ 0 0 form ] & = _ x 0 1 2^x+x 2^x 2-1 x & [ 0 0 form ] & = _ x 0 2^x 2+2^x 2+x ( 2^2 2^x . x & = _ x 0 2 2^x 2+2^x x ( 2^2 . x & =2 2 & Again, = _ x 0 x 2^x-x 1+x^2 - 1-x^2 & [ 0 0 form ] & = _ x 0 x 2^x-x 1+x^2 - 1-x^2 1+x^2 + 1-x^2 1+x^2 + 1-x^2 & [ 0 0 form ] & aligned aligned & = _ x 0 (x 2^x-x ) ( 1+x^2 + 1-x^2 ) 1+x^2-1+x^2 [ 0 0 form ] & = _ x 0 (z^x-1 ) [ 1+x^2 + 1-x^2 ] 2 x [ 0 0 form ] & = _ x 0 2^x 2 ( 1+x^2 + 1-x^2 )+ (z^x-1 ) 2 [ 2 x 1+x^2 - 2 x 1-x^2 ] & = 2(