2. For the following pairs of functions, determine which function grows faster. f(z) = 6r3 – 5a2 +9, g(x) = r³ log r %3D %3D (Use the limit theorem)
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- B) Find Maclaurin expression of the function y=f(x)%3D sin (x).find the value of xThe following is used to model a wave that impacts a concrete wall created by the US Navy speed boat.1. Derive the complete piecewise function of F(t) and F()The concrete wall is 2.8 m long with a cross-section area of 0.05 m2. The force at time equal zero is 200 N. It is also known that the mass is modeled as lumped at the end of 1200 kg and Young’s modulus of 3.6 GPa2. Use *Matlab to simulate and plot the total response of the system at zero initial conditions and t0 = 0.5 s
- Determine the function for the following sequence: 7, 12, 17, 22, 27, 32,... Please explain how you determined your solution. Please show work.3 : Prove that the sum of the three variables of the sum exponent f(x) = Σe is strictly convex. For this i=1 purpose, compute the Hessian matrix of the function f(x).6. (Stein's lemma) Suppose that X is normally distributed with mean u and variance o2. If g is a continuously differentiable function such that E{g(X)(X- µ)} and E{dg(X)/dx} both exist, prove that E{g(X)(X – u)} = o²E{dg(X)/dx}.