How to solve these two questions?

1.

Pierce is designing a sewage treatment plant using the new and innovative scronungeon valve. For this Pierce needs to calculate integrals of the form .3 In = theordx, n 20, and asks Harrison for a reduction formula to help. Harrison correctly finds a formula of the form In = antonIn-1, n21. Find Harrison's expressions for an and on and enter them down in the boxes below using Maple syntax. an = P bn = So that Pierce can verify Harrison's formula, Daniel Big Brain provides the following results. IA = 3 35355 e 24 818553 e24 4096 + 4096 and 15 = 15 32768 + 32768John decides to conduct a free fall experiment on the UNSW campus. He first buys a ball of mass m at the local Newsagent, then goes to the roof of a UNSW building at height H = 15 metres above the ground, and finally releases the ball. The ball falls towards the earth under gravity with air resistance equal to kv3/2 . John uses the fantastic Resisto Meter that he bought in the Future Store in Newtown to determine that k = 64. If 'v (9:) is the velocity of the ball at height a: above the ground, a model for the motion of the ball is d moi = mg 6403/2. John knows that the solution I) (2:) may be deduced from 'v mu :1: / _3d.= / 1dg, (1) C mg64u5 d but he needs your help to figure out some details. a) Enter the values for the lower limits c and d in the integrals, \"Em d=l:m b) Find the substitution 11 = h(u) that leads the integrand in the left hand side of (1) to become and write it in the box below. c) John uses the method of partial fractions to write rational functions f1 (u) and f2 (11.) such that 1 3 = f1(u)+ mu). mg 6411 By denoting (mg)1/3 = R, partial fractions yield f1(u) = 1131:; and f2 (u) = W for suitable polynomials P (u) and Q (u) Find P (u) and type your answer in the boxes below. PW) = I @ The polynomial Q (u) has the form Q(u) = Bu + 0. Enter the values for B and C in the boxes below. :lm Sm