math question

math question

Let 4 be the solution of the initial value problem y" - (2)y' + (-8)y =0, y(0) = 13, y'(0) = -2. Then lim1-+-00 4(x) Select one: O a. (-1) x (positive infinity) O b. (1) x (positive infinity) O c. None of these three d. existsGiven that P(4, 2) is a point of the graph of the equation In(x + ( - 3)y/2) + xy/2 = 4. If y = o(x) is a local solution of the equation around P, then o (4) is Select one: O a. 96 O b. 102 O c. None of these three O d. 106Let if x =0 f(x) = 1+ (sing(x)) sin(1/x) ifx 0 where g is a function over (-co, 0) U (0, too) with lime-0 g(x) = 0. Which of the following is TRUE? Select one: O a. None of these three. O b. f is continuous at 0 if a = 0. O c. f is continuous at 0 if a = 1. O d. f is discontinuous at 0 no matter what o is