Find the Taylor polynomial of order 4(four) generated by f(x) =x^1/3 at x=8

Modern high speed trains do not have perpendicular expansion gaps where rails are joined end-to-end any more they are mostly welded together but what might happen if there was a spell of particularly hot weather that causes inspection of the tracks?

Determine the time of the day and month of the year at which the peak sensible cooling load occurs for a top floor, north-eastern corner room of an office building in durban for the following conditions: floor area: 8 x 8 x 3 m east and north walls: 115 mm face brick (outside), 20 mm air space, 115 mm ordinary brick (inside) with 15 mm plaster roof construction: suspended plasterboard ceiling, 450 mm air space, 150 mm concrete, 75mm screed, waterproofing no heat transfer across other surfaces window area 3x 1,5 m high in north wall only. ordinary glass with venetian blinds. lights and occupants : from 07: 00 to 18: 00 average light density: 25 w/m2 number of occupants : 5 seated, light office work room temperature 24°c

Oxygen at 300 kpa and 400 k is in a closed system with an initial volume of 0.1 m3. is now compressed in a polytropic process, with exponent of n 1.2, to a temperature of 500 k. calculate: a) the boundary work done during the compression, in kj b) the heat transfer during the compression, in kj