This is a pure math problem about some special functions but you don't need to know any more about the functions than what is given here. you also shouldn't need to reach for maple, mathcad, or derive to solve these. an ordinary scientific calculator and the fundamental theorem of calculus should be enough the gamma function「(x) is a continuous and differentiable function for all positive values of x. it has the nifty property that for integer values ofx,「(-1)! (that's a factorial symbol, not a statement that i'm excited). so「(4) = 3! = 6,「(5) = 4! = 24, and so on. the digamma function ψ(x) is a continuous function defined as y(x) = in[f(x)] dx (which is probably just what you thought it would be using only a pocket calculator and the fundamental theorem of calculus, evaluate: 11.0 pcx) dx 7.0

As part of an industrial process, air as an ideal gas at 10 bar, 400k expands at steady state through a valve to a pressure of 4 bar. the mass flow rate of air is 0.5 kg/s. the air then passes through a heat exchanger where it is cooled to a temperature of 295k with negligible change in pressure. the valve can be modeled as a throttling process, and kinetic and potential energy effects can be neglected. (a) for a control volume enclosing the valve and heat exchanger and enough of the local surroundings that the heat transfer occurs at the ambient temperature of 295 k, determine the rate of entropy production, in kw/k. (b) if the expansion valve were replaced by an adiabatic turbine operating isentropically, what would be the entropy production? compare the results of parts (a) and (b) and discuss.

Marvin records scientific data about lake superior. for which property has marvin forgotten to use an si unit of measurement? shore length high temperature low temperature annual precipitation

Adolphin emits ultrasound at 100khz and uses the timing of reflections to determine the position of objects in the water. part a what is the wavelength of this ultrasound? assume that temperature of water is 20 degrees c. answer in cm