For each continuous function f on the interval [0, 1] let Tf

= be the function on [0, 1] defined by (Tf)(x) = e + 1 So* e2=tf(t) dt. a. Find a range of values for the parameter 1 for which the transformation T is a contraction with respect to the supremum norm given by || f || sup{f(t)[:te [0, 1]}. b. Find a range of values for the parameter 1 for which the transformation T 1/2 is a contraction with respect to the Lnorm given by || f ||2 c. Describe the iterative process for solving he integral equation f(x) = e. + 1 Sme2f(t) dt specifying the transformation to be iterated and explaining how this leads to a solution. With fo(x) 0 for all x as the starting function, compute the first three iterates f1(a), f2(x), and f3(x). = (15(t))* = = be the function on [0, 1] defined by (Tf)(x) = e + 1 So* e2=tf(t) dt. a. Find a range of values for the parameter 1 for which the transformation T is a contraction with respect to the supremum norm given by || f || sup{f(t)[:te [0, 1]}. b. Find a range of values for the parameter 1 for which the transformation T 1/2 is a contraction with respect to the Lnorm given by || f ||2 c. Describe the iterative process for solving he integral equation f(x) = e. + 1 Sme2f(t) dt specifying the transformation to be iterated and explaining how this leads to a solution. With fo(x) 0 for all x as the starting function, compute the first three iterates f1(a), f2(x), and f3(x). = (15(t))* =