Syntax advice: Use Maple syntax throughout this question except for essay boxes in which Maple syntax is not required. You can use the preview button next to any entry field to make sure that your syntax is correct. For the MATH1131 final exam preparation, Binwei and Haoyu challenge each other by coming up with their own improper integral and ask each other about the convergence of their integral. (a) Binwei came up with the integral I(p) = 8 + 5 - 8 - 5 d and asked Haoyu to give the largest interval for p such that I(p) converges. Haoyu realises that, by utilising the identity a3 - 63 a-b= a2 + ab + 62 the integrand can be rewritten as A(x) = 2 x 5P (xP + 5p)" + g(x) + (xP - 5p)n (1) where n = Number and g(@) = This lets Haoyu compare the function A() with another function B(x) such that lim A(I) 1+00 B(z) Click for List so Haoyu must have Click for List in their mind. Haoyu then chooses B(x) = Br* where B = and k = Therefore the largest interval for p such that I(p) converges is Syntax advice To enter the interval (1, 2] , type (1, 2]. . To enter the value co or -co type infinity or -infinity. (b) Now it is Haoyu's turn to challenge Binwei. They came up with the integral I(9) = 6 - dr 1+ 2 + x29+ 239 +...+ 299 + x10q and asked Binwei to give the largest interval for q such that I(q) diverges. Binwei proposes to simplify the integrand by realising both the numerator and denominator as Click for List . The integrand therefore can be written more compactly as C(x) = Syntax advice: For C() above, use the preview icon to the right of the entry box to make sure your Maple syntax is correct, for example, you have used brackets correctly and * for multiplications. Looking at this simplified form, Binwei claims that I(q) diverges for Click for List Help Binwei justify their answer below. Make sure you include any theorem that you use