1. Use the appropriate differentiation formulas to determine approximations that will complete the following table x 1 2 3 4 f(x) 1.46869 -6.14986 -59.65359 -142.75093 f (x) f (x) 2 Find the integral Sols by the Simpson 1/3 rule with 6 segment. 3. A particle of mass m moving through a fluid is subjected to a viscous resistance R, which is a function of the velocity v. The relationship between the resistance R, velocity v, and time t is given by the equation - PR m dv. R(V) vo Suppose that R(v) = -v vv for a particular fluid, where R is in newtons and v in m/s. If m - 5 kg and vo = 12 m/s, approximate the time t required for the particle to slow to vi = 8 m/s using Simpson 1/3 rule with 8 subintervals. 4. Calculate f (3.4) using Newtons interpolating polynomials of order 1 through 3 and estimate the error for the 1st, 2nd and 3rd order. f (x) 5 6.5 7