Could someone please check this work and let me know if it's correct and also answer the circled questions

Show That f ( x ) is not uniformly continuous on ( 0, 2 ) using E and S. 2. f (z) = - on (0, 2). Hint: First prove that - 0. > > Is This port necessary ? Then prove that - 2 - for a > 0. ey Show that | - 1 for a E (0, 1). y Let & = 1 and x = min (6,0.4) > Shouldn't This be !? What happens if y = 1 - 20 - ? Since e" is increasing when x > 0 , then e > e , which means - > - for all a > 0. Is This The right number, and if so, Thus, Let & = 1 . Then, given any 8 > 0 , letx = min {8, 0.4} and y = Then why ? 1 - x Shouldn't it be 1 ? Then, if x, y E (0, 2) and |ac - yl = 2- 1 ( 1 -x)x -2 20 - 20 2 = - x 1-x 1-x |1 - x] we have If ( 20) - f(y)1 = e's > 1 since y = 1 - x 1 = 1+ = 1 = E Thus, f is NOT uniformly continuous on (0, 2) by definition 5.4.1