4. A 1-D heat diffusion problem is given defined by: T T at with T(0,t)=100C T(10, t) = 50C and T(x,0)=0 C x2 0x10cm t0 t0 0x10 dT a) Graphically derive forward and backward difference approximations for dx (4 Marks) b) Use these forward and backward difference approximations to derive a central dT difference for (4 Marks) T c) By making the appropriate choice of difference formula for OT explicit finite difference formula for the PDE at - t> 0 aT x :0 at - and 0T Ox derive an (4 Marks) d) Taking c = 0.82, a step size in x of h = 2.5 and a time step k = 2 seconds estimate what the value of T will be at the grid points at time t = 2 seconds. (8 Marks)