Question 4 (Beta reduction and alpha renaming). For each of the following expressions, give the resulting redex after the highlighted redex is reduced. If there is need for renaming, you should break you answer into two parts. In the first part you do the renaming and in the second part you do the beta reduction. In all cases, you should highlight by using bolface the whole part of the result that corresponds to the redex after it is reduced. Also, if alpha renaming is needed, you should highlight the whole redex with the par that is renamed.

1. (λx. x x)(λx. x )
2. (λx. x x)(λx. y )

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Asteam is contained in a rigid tank with a volume of 1 m3. initially, the pressure and temperature are 7 bar and 500 oc, respectively. the temperature drops due to cooling process. determine: (1) the temperature at which condensation begins in °c, (2) the fraction of the total mass that has condensed when the pressure decreased to 0.5 bar. (3) the volume in m3 occupied by saturated liquid at the final state?

The short distance from the objective lens to the object causes problems at high magnification. which of the following is the most serious? a. cleaning the object surface b. positioning the object c. reflection from the object surface. d. illumination of the object