Consider a function f(x) = 25x ଷ − 6x ଶ + 7x − 88. Using the Taylor series expansions of this functions from zero- through third-order, predict the value of f(x) with x = 3 using a base point of x଴ = 1.0. For each such Taylor series approximation, list the following: (i) Approximate value of f(3.0).
(ii) On what order of the step size ‘h’ is the truncation error?
(iii) Compute the true percent relative error,t , for each approximation.

Two flowing streams of argon gas are adiabatically mixed to form a single flow/stream. one stream is 1.5 kg/s at 400 kpa and 200 c while the second stream is 2kg/s at 500 kpa and 100 ? . it is stated that the exit state of the mixed single flow of argon gas is 150 c and 300 kpa. assuming there is no work output or input during the mixing process, does this process violate either the first or the second law or both? explain and state all your assumptions.

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.

Determine whether or not it is possible to compress air adiabatically from k to 140 kpa and 400 k. what is the entropy change during this process?