For this problem, you will be writing an _automatic differentiation_ method that, given an expression `e` which involves just a single identifier `x` (no need to check this fact), will return an expression for `de/dx`, the derivative of `e` with respect to `x`.

Precipitation hardening can be achieved in many light alloys by a three-step heat treatment. what is carried out and what is the purpose at each step? why is such a treatment necessary based on the nucleation and growth theory of phase transformation. compare this treatment with tempering martensite for carbon steels (similarities and differences).

An array of m-50 thermoelectric modules is installed on the exhaust of a sports car. each module has an effective seebeck coefficient of sp of 0.143 5vk and an internal electrical resistance of r.-4 ? in addition, : (15 points each module is of width w 60mm and contains n=100 pairs of semiconducting pellets. each pellet hasan overall length of 2l-5mm and a cross-sectional area as 1.2 x 10'm and is characterized by a thermal conductivity of kpl2w rnk. the hot side of each module is exposed to exhaust gases at·p650c with hia4ow rrk while the osite side of each module is cooled by pressurized water at surface) and 156 °c (at the cool surface). 11s c with h: -500w/m'k. the modules are wired n series and the load resistance is r d=400ohm .the module surface temperatures, t, and ts are 183 "c (at the hot surface and 156c (at the cool surface) a)-draw a schematic of this scenario and label all parts. a. b. if the induced current, i, is 0.15 amps, what is the total power (pa) for one module? c. what is the total power harvest from the exhaust with all 50 modules?

Aflow moves in the x direction with a velocity of 10 m/s from 0 to 0.1 second and then reverses direction with the same speed from 0.1 to 0.2 second. sketch the pathline strating from x-0 and the streak! ine with dye introduced at x=0. show the streamlines for the first time interval and the second time interval.