3. (25 pts.) Compute the first four polynomial interpolations (linear, quadratic, etc.) for the function $(x) = 1 - exp(-x) with evenly spaced data on the interval x € (0,3). Make a plot of the

interpolation and the function itself using MATLAB. Also make a plot of the difference between

the function and the interpolant. You can either work it out by hand or by writing a program. If

you work it out by hand, include the values of all the coefficients for each interpolation formula.

When at a point two solid phase changes to one solid phase on cooling then it is known as a) eutectoid point b) eutectic point c) peritectic point d) peritectoid point

Apiston-cylinder with a volume of 0.25 m3 holds 1 kg of air (r 0.287 k/kgk) at a temperature of 100 c. heat transfer to the cylinder causes an isothermal expansion of the piston until the volume triples. how much heat is added to the piston-cylinder?

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.